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In this paper, we study the annihilating properties of ideals generated by coefficients of polynomials and power series which satisfy a structural equation. We first show that if f (x) R g (x) = 0 for polynomials f (x) = ∑ i = 0 m a i x i , g (x) = ∑ j = 0 m b j x j over any ring R , then for any i , j , there exist positive integers s (i , j) and t (i , j) such that a i 1 R a i 2 R ⋯ a i s (i , j) R b j = 0 and a i R b j 1 R b j 2 R ⋯ R b j t (i , j) = 0 , whenever i 1 , i 2 , ... , i s (i , j) ≤ i and j 1 , j 2 , ... , j t (i , j) ≤ j. Next we prove that if f (x) R g (x) = 0 for power series f (x) = ∑ i = 0 ∞ a i x i , g (x) = ∑ j = 0 ∞ b j x j over any ring R , then for any i , j , there exist positive integers s (i , j) and t (i , j) such that a i s (i , j) R ⋯ R a i 2 R a i 1 R b j 1 R b j 2 R ⋯ R b j t (i , j) = 0 when ∑ p = 1 s (i , j) i p + ∑ q = 1 t (i , j) j q < (s (i , j) + 1) (t (i , j) + 1) (i + 1) (j + 1) and i p ≤ i , j q ≤ j for each p , q. [ABSTRACT FROM AUTHOR]

We prove that it is relatively consistent with \mathsf {ZFC} that every maximal ideal is Katětov above of all F_\sigma ideals. In particular, we prove that it is consistent that there is no Hausdorff ultrafilter. The main theorem answers questions from Mauro Di Nasso and Marco Forti [Proc. Amer. Math. Soc. 134 (2006), pp. 1809–1818], Jana Flašková [WDS'05 proceedings of contributed papers: part I - mathematics and computer sciences, 2005; Comment. Math. Univ. Carolin. 47 (2006), pp. 617–621; 10th Asian logic conference, World Sci. Publ., Hackensack, NJ, 2010], Osvaldo Guzmán and Michael Hrušák [Topology Appl. 259 (2019), pp. 242–250], and Mauro Di Nasso and Marco Forti [Logic and its applications, Contemp. Math., Amer. Math. Soc., Providence, RI, 2005], and gives a different model for a question from Michael Benedikt [J. Symb. Log. 63 (1998), pp. 638–662], which was originally solved by S. Shelah [Logic colloquium '95 (Haifa), lecture notes logic, Springer, Berlin, 1998]. [ABSTRACT FROM AUTHOR]

The structure theorems for (Completely) simple semigroups and (Completely) 0-simple semigroups have proved a powerful tool in the investigation of such semigroups. In this paper, first of all, we define weak simple semigroups and weak 0-simple semigroups and compare them with simple semigroups and 0-simple semigroups respectively. Then we give examples of these semigroups and describe the structure of them. Also, we define completely weak simple semigroup and completely weak 0-simple semigroup. Finally, by using Green's equivalences, we prove some results and give equivalences, for these semigroups. [ABSTRACT FROM AUTHOR]

In this paper, we characterize those rings A and complete Brouwerian residuated lattices L whose residuated lattice F i d (A , L) , of L-fuzzy ideals of A , forms a Boolean algebra. [ABSTRACT FROM AUTHOR]

The French linguistic factor exerted pressure in the different stages of the evolution of the Romanian language, enriching and dynamizing it, accelerating its evolution. But the imitative excess leads to a reaction of rejection. The myth is denounced, the model of the perfect language is subjected to criticism. The interaction between the two languages gives rise, over time, to a different imaginary. It reflects the subjective and self-reflexive perspective of the Romanian speaker. In our paper, we will analyze the relevance of the theory of the linguistic imaginary from this perspective. [ABSTRACT FROM AUTHOR]

This paper is a continuation of ideas presented by Bagirmaz (Appl Algebra Eng Commun Comput 30(4):285–297, 2019). Indeed, we introduce the notion of near approximations in a ring, which is an extended notion of a rough approximations in a ring. Then we define lower and upper near subrings based on ideals in a ring and give some properties of such subrings. Furthermore, we obtain a comparison between these types of approximations and the approximations introduced by Davvaz (Inf Sci 176:2417–2437, 2006). [ABSTRACT FROM AUTHOR]

The notions of ideals and filters have studied in many algebraic (crisp) fuzzy structures and used to study their various properties, representations and characterizations. In addition to their theoretical roles, they have used in some areas of applied mathematics. In a recent paper, Arockiarani and Antony Crispin Sweety have generalized and studied these notions with respect to the concept of neutrosophic sets introduced by Smarandache to represent imprecise, incomplete and inconsistent information. In this article, we aim to deepen the study of these important notions on a given lattice in the neutrosophic setting. We show their various properties and characterizations, in particular, we pay attention to their characterizations based on of the lattice min and max operations. In addition, we study the notion of prime single-valued neutrosophic ideal (respectively, filter) as interesting kind and we discuss some its set-operations, complement and associate sets. [ABSTRACT FROM AUTHOR]

In this paper, entries of sequences, infinite series and infinite matrices are real or complex numbers. We prove some interesting properties of the matrix classes (co, c) and (co, c; P). [ABSTRACT FROM AUTHOR]

Let (S, ·, ≤) be an ordered semigroup and let A be a nonempty subset of S. The radical of A, denoted √A, is √A = {x ∈ S | xn ∈ A for some positive integer n}. The paper characterizes when the radical √Q is a subsemigroup of S for all quasi-ideals Q of S. [ABSTRACT FROM AUTHOR]

Let T(X) be the full transformation semigroup on the set X . For a fixed nonempty subset Y of X, let PGY (X) = {α ∈ T(X) : α|Y ∈ G(Y )} where G(Y ) is the permutation group on Y . It is known that P GY (X) is a regular subsemigroup of T(X). In this paper, we give a simpler description of Green’s relations and characterize the ideals of P GY (X). Moreover, we prove some isomorphism theorems for PGY (X). For finite sets, we investigate the cardinalities of PGY (X) and of its subsets of idempotents, and we also calculate their ranks. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the concepts of para and quasi topological MV -algebras, which was first introduced by Najafi et al. in 2017, to BL-algebras as para and quasi topological BL-algebras and elaborate these concepts via some examples. We further derive and prove some theorems by employing pre-filters and a fundamental system of neighborhoods. [ABSTRACT FROM AUTHOR]

In random experiments, the fact that the sets of events has a structure of a Boolean algebra, i.e. it follows the rules of classical logic, is the main hypothesis of classical probability theory. Bosbach states have been introduced on commutative and non-commutative algebras of fuzzy logics as a way of probabilistically evaluating the formulas. In this paper, we focus on the relationship between some properties of ideals and Bosbach states in the framework of commutative residuated lattices. In particular, we introduce the concept of co-kernel of a Bosbach state which is an ideal and we establish the relationship between the notion of co-kernel and the kernel. Moreover, we define and characterize maximal ideals and maximal MV-ideals in residuated lattices. [ABSTRACT FROM AUTHOR]

Farthest point problem states that "Must every uniquely remotal set in a Banach space be singleton?" In this paper we introduce the notion of partial ideal statistical continuity of a function which is way weaker than continuity of a function. We give an example to show that partial ideal statistical continuity is weaker than continuity. In this paper we use Ideal summability to give some answers to FPP problem which improves the result in [13]. We prove that if E is a non-empty, bounded, uniquely remotal subset in a real Banach space X such that E has a Chebyshev center c and the farthest point map F : X → E restricted to [c, F(c)]? is partially ideal statistically continuous at c then E is singleton. [ABSTRACT FROM AUTHOR]

Let R be a commutative semiring with 1 ≠ 0 , M an R-semimodule, and n ≥ 1 a positive integer. A proper subsemimodule P of M is called n-absorbing, if whenever r 1 , ... , r n ∈ R and x ∈ M together with r 1 ... r n x ∈ P , imply r 1 ... r n ∈ (P : M) or there exists 1 ≤ i ≤ n such that r 1 ... r i ^ ... r n x ∈ P . In this paper, we study the concept of n-absorbing subsemimodules that is a generalization of prime subsemimodules. Some basic properties of these subsemimodules and some useful examples of them are investigated. Also, we study the stability of n-absorbing subsemimodules with respect to some various constructions of semimodules. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of I and I-convergence of sequences in gradual normed linear spaces. We study some basic properties and implication relations of the newly defined convergence concepts. Also, we introduce the notions of I and I-Cauchy sequences in the gradual normed linear space and investigate the relations between them. [ABSTRACT FROM AUTHOR]

Let H be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed field of characteristic zero. In this paper we show that any finite-dimensional indecomposable H -module is generated by one element. In particular, any indecomposable submodule of H under the adjoint action is generated by a special element of H. Using this result, we show that the Hopf algebra H is a principal ideal ring, i.e., any two-sided ideal of H is generated by one element. As an application, we give explicitly the generators of ideals, primitive ideals, maximal ideals and completely prime ideals of the Taft algebras. [ABSTRACT FROM AUTHOR]

In this paper we mainly deal with I(q) c -convergence. In particular we study bounded multipliers of bounded I(q) c -convergent sequences. We also give some I-core results and characterize the inclusion K-core {Ax} ⊆ I-core {x} for bounded sequences x = (xn). [ABSTRACT FROM AUTHOR]

In this paper we study Morita contexts between rings without identity. We prove that if two associative rings are connected by a Morita context with surjective mappings, then these rings have isomorphic quantales of unitary ideals. We also show that the quotient rings by ideals that correspond to each other under that isomorphism are connected by a Morita context with surjective mappings. In addition, we consider how annihilators and two-sided socles behave under that isomorphism. [ABSTRACT FROM AUTHOR]

In this paper, we have given I2-lacunary statistical convergence and strongly I2-lacunary convergence with regards to the intuitionistic fuzzy norm (µ, v), investigate their relationships, and make some observations about these classes. Also, we have examined the relation between these two new methods and the relation between I2-statistical convergence in the corresponding intuitionistic fuzzy normed space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of 0-distributivity and 1-distributivity in join semilattices. We give some characterizations of 0-distributive join semilattices. We prove Stone type separation theorem for 0-distributive and 1-distributive join semilattices. 0-distributive normal and comaximal join semilattices have been introduced. We show that the class of 0-distributive normal join semilattice is proper super class of 0-distributive comaximal join semilattices. We also show that in presence of 1-distributivity class of 0-distributive normal and comaximal join semilattices are equivalent. [ABSTRACT FROM AUTHOR]

In this paper, the notion of minimal prime ideal is introduced in residuated lattices and related properties are investigated. Also, new equivalent characterizations and properties for prime and maximal ideals are obtained and the relation between these ideals and minimal prime ideals is discussed for De Morgan residuated lattices. Moreover, we prove that it is possible to introduce and study, by a standard way, Zariski topology on the lattice P (L) of prime ideals of any residuated lattice L. Also, since m P (L) , the set of minimal prime ideals of L , and M (L) , the set of maximal ideals of L , are subsets of P (L) , we endow m P (L) and M (L) with the topology induced by the Zariski topology on P (L) and we characterize these topological spaces for residuated lattices. [ABSTRACT FROM AUTHOR]

We study ideal cotorsion pairs associated to almost exact structures in extension closed subcategories of triangulated categories. This approach allows us to extend the recent ideal approximation theory developed by Fu, Herzog et al. for exact categories in the above mentioned context. In the last part of the paper we apply the theory in order to study projective classes (in particular localization or smashing subcategories) in compactly generated triangulated categories. [ABSTRACT FROM AUTHOR]

Recently Bukovský, Das and Šupina [Ideal quasi-normal convergence and related notions, Colloq. Math. 146 (2017), 265–281] started the study of sequence selection properties (𝓘, 𝓙-α1) and (𝓘, 𝓙-α4) of Cp(X) using the double ideals, where 𝓘 and 𝓙 are the proper admissible ideals of ω, which are motivated by Arkhangeľskii local αi-properties [The frequency spectrum of a topological space and the classification of spaces, Dokl. Akad. Nauk SSSR 13 (1972), 1185–1189]. In this paper, we obtain some characterizations of (𝓘, 𝓙-α1) and (𝓘, 𝓙-α4) properties of Cp(X) in the terms of covering properties and selection principles. Under certain conditions on ideals 𝓘 and 𝓙, we identify the minimal cardinalities of a space X for which Cp(X) does not have (𝓘, 𝓙-α1) and (𝓘, 𝓙-α4) properties. [ABSTRACT FROM AUTHOR]

We say that an ideal ℐ has property (T) if for every ℐ-convergent series ∑ n = 1 ∞ x n , there exists a set A ∈ ℐ such that Σn∈ℕ\Axn converges in the usual sense. The aim of this paper is to construct a nontrivial ideal with property (T) under the assumption that cov (ℳ) = c. [ABSTRACT FROM AUTHOR]

The problem of 'applicability' of mathematics to modern physical sciences has been labeled as an 'unreasonably effective' and unexplainable 'miracle' by prominent physicists such as Eugene Wigner and Paul Dirac. Philosophers of science from contending traditions have also contributed to the debates at large. While some have tried to trivialize the problem, others, in particular those with a phenomenological orientation, have attempted to eliminate this riddle, claiming that the two domains are 'identical'. This paper, while challenging some of these interpretations, proposes a solution from a dialectical materialist position. Drawing on Evald Ilyenkov's concept of the 'ideal' as the objectivized form of human activity in social nature, it is suggested that the two realms are necessarily interconnected as schemata of human activity which aim for a highly quantified conceptualization of reality. [ABSTRACT FROM AUTHOR]

The present paper highlights the agricultural consortium: It is a study of Consortium for e-resources in Agriculture (CeRA) which is an initiative from ICAR for the agricultural libraries of country as well as libraries of Chhattisgarh. The study is based problem and prospects in utilization of digital information resources of CeRA in IGKV Raipur Chhattisgarh during COVID-19. The outcome and findings are very positive and effective. Some problems are observed in remotely located agricultural libraries of Chhattisgarh but the facility in urban areas are very good, maximum use of CeRA through DDR by the users Chhattisgarh. Resources of various discipline/subject coverage CeRA are broad. CeRA meet the academic and research needs of faculty, research scholars and students across the country as well as Chhattisgarh. Now the time has come to think about how to strengthen for more useful CeRA facility to each and every corner of country in wider range through remote access software's or cloud computing etc. Need increase more e-resources in CeRA, financial support for maintain Consortium and collaboration of agricultural libraries. Agricultural Libraries of India as well as Chhattisgarh should also up to date from latest e-Resources and its facilities to achieve the object for which they are established. [ABSTRACT FROM AUTHOR]

This paper is devoted to studies of I wQN-spaces and some of their cardinal characteristics. Recently, Šupina in [32] proved that I is not a weak P-ideal if and only if any topological space is an I QN-space. Moreover, under p = c he constructed a maximal ideal I (which is not a weak P-ideal) for which the notions of I QN-space and QN-space do not coincide. In this paper we show that, consistently, there is an ideal I (which is not a weak P-ideal) for which the notions of I wQN-space and wQN-space do not coincide. This is a partial solution to [6, Problem 3.7] . We also prove that for this ideal the ideal version of Scheepers Conjecture does not hold (this is the first known example of such weak P-ideal). We obtain a strictly combinatorial characterization of non ( I wQN-space ) similar to the one given in [32] by Šupina in the case of non ( I QN-space ) . We calculate non ( I QN-space ) and non ( I wQN-space ) for some weak P-ideals. Namely, we show that b ≤ non ( I QN-space ) ≤ non ( I wQN-space ) ≤ d for every weak P-ideal I and that non ( I QN-space ) = non ( I wQN-space ) = b for every F σ ideal I as well as for every analytic P-ideal I generated by an unbounded submeasure (this establishes some new bounds for b ( I , I , Fin ) introduced in [31] ). As a consequence, we obtain some bounds for add ( I QN-space ) . In particular, we get add ( I QN-space ) = b for analytic P-ideals I generated by unbounded submeasures. By a result of Bukovský, Das and Šupina from [6] it is known that in the case of tall ideals I the notions of I QN-space ( I wQN-space) and QN-space (wQN-space) cannot be distinguished. Answering [6, Problem 3.2] , we prove that if I is a tall ideal and X is a topological space of cardinality less than co v ⁎ ( I ) , then X is an I wQN-space if and only if it is a wQN-space. [ABSTRACT FROM AUTHOR]

In recent years, the Fuzzy theory has emerged as the most active area of research in many branches of mathematics and engineering. This new theory was introduced by L.A. Zadeh in 1965 and since then large number of research papers have been appeared by using the concept of Fuzzy set/numbers and fuzzification of many classical theories has also been made. The object of this paper is to define the intuitionistic Fuzzy I-convergent double sequence spaces 2SI(μ,v)(T, f ) and 2SI (μ,v)0(T, f ) defined by Compact Operator and Modulus Function. We study some topological and algebraic properties of these spaces and discuss the Fuzzy topology on them. [ABSTRACT FROM AUTHOR]

This paper is an extension of our paper I-cluster points of filters [8]. In this paper, we have discussed the relationship between I-cluster points of filters and cluster points of nets and estabilished their equivalence.We have also estabilished the equivalence of I-cluster points of filters and nets. [ABSTRACT FROM AUTHOR]

In this paper, we have introduced the concept of I-cluster point of a filter on a topological space and studied its various properties. We have proved the necessary condition for a filter to have an I-cluster point. Most of the work in this paper is inspired from [2] and [23]. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to extend Flanigan's theorem in [4] concerning ideal essential extensions of rings to left ideal essential extensions. Moreover, we give new proofs of two Flanigan's theorems and answer a question raised by M. Petrich in [5] which is related to pure extensions of rings. [ABSTRACT FROM AUTHOR]

In random experiments, the fact that the sets of events has a structure of a Boolean algebra, i.e. it follows the rules of classical logic, is the main hypothesis of classical probability theory. Bosbach states have been introduced on commutative and non-commutative algebras of fuzzy logics as a way of probabilistically evaluating the formulas. In this paper, we focus on the relationship between some properties of ideals and Bosbach states in the framework of commutative residuated lattices. In particular, we introduce the concept of co-kernel of a Bosbach state which is an ideal and we establish the relationship between the notion of co-kernel and the kernel. Moreover, we define and characterize maximal ideals and maximal MV-ideals in residuated lattices. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of neutrosophic ℵ-bi-ideal for a semigroup. We infer different semigroups using neutrosophic ℵ -bi-ideal structures. Moreover, for regular semigroups, neutrosophic ℵ-product and intersection of neutrosophic ℵ-ideals are identical. [ABSTRACT FROM AUTHOR]

In this paper, we define the notion of EBL-algebras, which are generalizations of BL-algebras and EMV-algebras. The notions of ideals, congruences and filters in EBL-algebras are introduced, and their mutual relationships are investigated. There is a one-to-one correspondence between the set of all ideals in an EBL-algebra and the set of all congruences on an EBL-algebra. Moreover, we give a representation theorem on EBL-algebras. Every proper EBL-algebras under some condition can be embedded into an EBL-algebras with a top element as an ideal. [ABSTRACT FROM AUTHOR]

This paper aims to introduce quasi-ideals and bi-ideals of ſ-seminearrings. Some related properties are investigated, and some relations between quasi-ideals and bi-ideals are shown. Besides, the smallest (right/left/quasi-) ideal of ſ-seminearrings is characterized. [ABSTRACT FROM AUTHOR]

In this paper we have introduced a new type of sets termed asμ-open sets which unifies semiopen sets and discussed some of its properties. We have also introduced another type of weak open sets termed as Iμ-open sets depending on a GT as well as an ideal on a topological space. Finally the concept of weakly Iτ - open sets are investigated. [ABSTRACT FROM AUTHOR]

As we have already seen in Turkish Journal of Mathematics (2019) 43: 2592--2601 many results on hypersemigroups do not need any proof as they can be obtained from lattice ordered semigroups. The present paper goes a step further, to show that many results on Γ-hypersemigroups as well can be obtained from lattice ordered semigroups. It can be instructive to prove them directly, but even in that case the proofs go along the lines of lattice ordered semigroups (or poe-semigroups). In the investigation, we faced the problem to correct the definition of Γ-hypersemigroups given in the existing bibliography. [ABSTRACT FROM AUTHOR]

In terms of ideals, this paper investigates ordered semigroups satisfying certain regularity conditions. In particular we study regularity, complete regularity, quasi-regularity, intra-regularity as well as left (right) regularity, left (right) quasi-regularity, and left (right) reproduce. [ABSTRACT FROM AUTHOR]

For a non-empty subset A of a semigroup S, ... denotes the radical of A, i.e., ... for some positive integer ng. This paper characterizes when the radical ... is a subsemigroup of S for every quasi-ideal Q of S. [ABSTRACT FROM AUTHOR]

In an earlier work, the authors prove Stillman's conjecture in all characteristics and all degrees by showing that, independent of the algebraically closed field K or the number of variables, n forms of degree at most d in a polynomial ring R over K are contained in a polynomial subalgebra of R generated by a regular sequence consisting of at most ηB(n,d) forms of degree at most d; we refer to these informally as ''small'' subalgebras. Moreover, these forms can be chosen so that the ideal generated by any subset defines a ring satisfying the Serre condition Rη. A critical element in the proof is to show that there are functions ηA(n,d) with the following property: in a graded n-dimensional K-vector subspace V of R spanned by forms of degree at most d, if no nonzero form in V is in an ideal generated by ηA(n,d) forms of strictly lower degree (we call this a strength condition), then any homogeneous basis for V is an Rη sequence. The methods of our earlier work are not constructive. In this paper, we use related but different ideas that emphasize the notion of a key function to obtain the functions ηA(n,d) in degrees 2, 3, and 4 (in degree 4 we must restrict to characteristic not 2, 3). We give bounds in closed form for the key functions and the ηA functions, and explicit recursions that determine the functions ηB from the ηA functions. In degree 2, we obtain an explicit value for ηB(n,2) that gives the best known bound in Stillman's conjecture for quadrics when there is no restriction on n. In particular, for an ideal I generated by n quadrics, the projective dimension R/I is at most 2n+1(n − 2) + 4. [ABSTRACT FROM AUTHOR]

In 1988, given a complete Brouwerian lattice L : = (L ; ∧ , ∨ ; 0 , 1) and a ring A : = (A ; + , · ; - ; 0) with unity 1, Swamy and Swamy (J Math Anal Appl 134:94–103, 1988) built a lattice structure, on the set of L-fuzzy ideals of A , and investigated some of its arithmetic properties. Since the residuation theory is richer than the lattice theory [see, Ciungu (Non-commutative multiple-valued logic algebras, Springer monographs in mathematics, Springer, Berlin, 2014), Galatos et al. (An algebraic glimpse at substructural logics, volume 151 of studies in logic and the foundations of mathematics, Elsevier, Amsterdam, 2007), Jipsen and Tsinakis (in: Martinez (ed) Ordered algebraic structures, Kluwer Academic Publisher, Dordrecht, 2002), Piciu (Algebras of fuzzy logic, Editura Universitaria Craiova, Craiova, 2007)], in this paper, we consider the notion of fuzzy ideals rather under a complete Brouwerian residuated lattice L : = (L ; ∧ , ∨ , ⊖ , ↠ , ⊸ ; 0 , 1) . A residuated lattice F i d (A , L) : = (F i d (A , L) ; ∧ , + , ⊗ , ↪ , ↬ ; χ 0 , 1 ̲) is built on the set F i d (A , L) of L-fuzzy ideals of A and it is shown that the latter is both an extension of L and the residuated lattice I d (A) : = (I d (A) ; ∩ , + , ⊙ , → , ⇝ ; { 0 } , A) on the set I d (A) of ideals of A . [ABSTRACT FROM AUTHOR]

In the present paper, by considering the notion of ideals in MV -algebras, we study some kinds of ideals in MV -algebras and obtain some results on them. For example, we present definition of ultra ideal in MV -algebras, and we get some results on it. In fact, by definition of ultra ideals, we present new conditions to have prime ideals, positive implicative ideals and maximal ideals in MV -algebras. Also, we state some properties on contracted or extended ideals as useful examples of ideals in MV -algebras. Finally, we try to prove the Chines reminder theorem in MV -algebras. [ABSTRACT FROM AUTHOR]

In this paper, we define the notion of a pseudo-eBE-algebra as an extension of a pseudo-BE-algebra, and it is studied in detail. The construction of an eBE-algebra from a pseudo-eBE-algebra is given. Further, the notions of filters and ideals are considered. The classes of distributive and commutative pseudo-eBE-algebras are introduced and investigated. We prove that for a distributive pseudo-eBE-algebra filters coincide with ideals. Also, some types of filters are defined and the relationship between these is investigated. [ABSTRACT FROM AUTHOR]

In this paper, congruences, ideals, and prime ideals of an EMV-semiring and of its associated EMV-algebra are studied. Then EMV-semirings are characterized and it is proved that each EMV-semiring can be embedded into a direct product of a family of MV-semirings as an EMV-semiring. Moreover, another representation of EMV-semirings are presented by EMV-semirings of continuous sections in a sheaf of commutative semirings whose stalks are localizations of EMV-semirings over prime ideals. Also, using the categorical equivalence between EMV-semirings and EMV-algebras, a representation of EMV-algebras are obtained. [ABSTRACT FROM AUTHOR]