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Giving the proper citations, it is shown that, except of Lemma 2.4 and Theorem 2.6, almost all the results of the paper in the title have been previously published for ordered hypersemigroups in Eur. J. Pure Appl. Math. and they are not new. There are also two results obtained from ordered semigroups just putting a "o" instead of "o" (that isn't a correct way to work), without reference to ordered semigroups on which the results on ordered hypersemigroups are based. One of them can be obtained as corollary to a theorem in Eur. J. Pure Appl. Math. as well, and it is not new. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of I-convergence of sequences of k-dimensional subspaces of an inner product space, where I is an ideal of subsets of N, the set of all natural numbers and k ∈ N. We also study some basic properties of this notion. [ABSTRACT FROM AUTHOR]

In this paper, we defined the concepts of lacunary I∗-convergence and strongly lacunary I∗-convergence. We investigated the relations between strongly lacunary I-convergence and strongly lacunary I∗- convergence. Also, we defined the concept of strongly lacunary I∗-Cauchy sequence and investigated the relations between strongly lacunary I-Cauchy sequence and strongly lacunary I∗-Cauchy sequence. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to introduce the notion of stabilizers in L-algebras and develop stabilizer theory in L-algebras. In this paper, we introduced the notions of left and right stabilizers and investigated some related properties of them. Then, we discussed the relations among stabilizers, ideal and co-annihilators. Also, we obtained that the set of all ideals of a CKL-algebra forms a relative pseudo-complemented lattice. In addition, we proved that right stabilizers in CKL-algebra are ideals. Then by using the right stabilizers we produced a basis for a topology on L-algebra. We showed that the generated topology by this basis is Baire, connected, locally connected and separable and we investigated the other properties of this topology. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the classes of α and strictly-α seminearrings and establishes some of their properties, mostly in relation to the possession of a mate function. Then we get the criterion for an α-seminearring to become a strictly-α seminearring. We also obtain a complete characterisations of α and strictly-α seminearrings and proved certain results for α and strictly-α seminearrings via certain unique classes of seminearrings. [ABSTRACT FROM AUTHOR]

This is about the paper "Bi-interior ideals of semigroups" by M. Murali Krishna Rao in Discuss. Math. Gen. Algebra Appl. 38 (2018) 69–78. According to Theorem 3.11 (also Theorem 3.3(8)) of the paper, the intersection of a bi-interior ideal B of a semigroup M and a subsemigroup A of M is a bi-interior ideal of M. Regarding to Theorem 3.6, every bi-interior ideal of a regular semigroup is an ideal of M. We give an example that the above two results are not true for semigroups. According to the same paper, if M is a regular semigroup then, for every bi-interior ideal B , every ideal I and every left ideal L of S , we have B ∩ I ∩ L ⊆ B I L. The proof is wrong, we provide the corrected proof. In most of the results of the paper the assumption of unity is not necessary. Care should be taken about the proofs in the paper. [ABSTRACT FROM AUTHOR]

In this paper, we investigate r-ideals in commutative ordered semigroups with zero and identity. Moreover, we study some properties of r-ideals. Furthermore, we give several characterizations of r-ideals. [ABSTRACT FROM AUTHOR]

Recently, Milles and Hammami presented and studied the concept of a neutrosophic topology generated by a neutrosophic relation. As a continuation in the same direction, this paper studies the concepts of neutrosophic ideals and neutrosophic filters on that topology. More precisely, we offer the lattice structure of neutrosophic open sets of a neutrosophic topology generated via a neutrosophic relation and examine its different characteristics. Furthermore, we enlarge to this lattice structure the notions of ideals (respectively, filters) and characterize them with regard to the lattice operations. We end this work by studying the prime neutrosophic ideal and prime neutrosophic filter as interesting types of neutrosophic ideals and neutrosophic filters. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a c-prime fuzzy graph of a nearring with respect to a level ideal of a fuzzy ideal. We find a relation between properties of the fuzzy ideal and properties of the fuzzy graph. We introduce ideal symmetry of the fuzzy graph and obtain conditions under which the graph is ideal symmetric. We find a relation between nearring homomorphisms and graph homomorphisms. We investigate conditions required for the homomorphic image of a c-prime fuzzy ideal to be a c-prime fuzzy ideal. [ABSTRACT FROM AUTHOR]

In this paper, we introduce, graph of lower and upper approximation of a non-empty subset of a nearring with respect to an ideal. We relate the properties of these graphs with properties of ideals. We study the relationship between the connectivity of the graph and properties of the approximation set. We obtain the properties of these graphs under nearring homomorphism. [ABSTRACT FROM AUTHOR]

In this paper, we have introduced the notions of rough I-convergence of sequences and defined I-cluster point of a sequence and proved some results associated with this notion in 2-normed spaces. Also, we have defined rough I-limit set of a sequence and shown that this set is closed and convex. Further, we have defined the notion of rough I-Cauchy sequence in the same space. [ABSTRACT FROM AUTHOR]

Divisibility of elements in a semigroup and the decomposition of a semigroup into subdirect product of semigroups are two basic concepts in the study of the structure of semigroups. The main object of our present paper is to show that the divisibility of elements in a semigroup determines a decomposition of a semigroup of all fuzzy sets in into a subdirect product of semigroups, where the operation on is defined by the following way: for fuzzy set and in , if , and if . [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of Esemihoops, which is an extension of semihoops and Ehoops. We also give some related properties of these algebras. In addition, we define the notions of ideals, congruences and filters on Esemihoops and study the relations between them. There is a one-to-one correspondence between the set of all ideals and the set of all congruences on a regular Esemihoop. At the same time, it is proved that every proper Esemihoop has at least one maximal filter. For a regular Esemihoop A, A has at least one maximal ideal and every maximal ideal is prime. Furthermore, we prove that a Bosbach state on Esemihoops is a Riečan state. In particular, Bosbach states and Riečan states are consistent on Glivenko Esemihoops. Moreover, we show that there is a one-to-one correspondence between the set of t-compatible Riečan states on A and the set of Riečan states on t (A). Finally, the topology of the set of all prime state filters is established. [ABSTRACT FROM AUTHOR]

This paper examines how the Durkheimian approach to the 'ideal' delineates a possible way of straddling the dilemma between the normative orientation of 'powerful knowledge' accounts and the critical orientation of 'knowledge of the powerful' accounts. It argues that the normative aims are embedded in the fabrics of the sociological description with which the Durkheimian notion of 'elementary form' is concerned. To see where this enterprise can lead, this paper turns to the sociology of education of Bourdieu and Bernstein. Both draw on Durkheim's writings on primitive classifications in education and society, working towards uncovering the regularities of the world of knowledge classifications. Keeping in line with Bourdieu and Bernstein, this paper argues that one has to make the same refusal to the advocates of an abstract ideal of educational knowledge that is dissociated from its social conditions of historical realization in pedagogic contexts, and to the advocates of a cynical relativism of ideal that rejects any necessities socially established. [ABSTRACT FROM AUTHOR]

Through this paper, via the operators (.)* and ψ, we presented notion of *-Locally set in an ideal topological space Zi as a new stronger form of locally closed set, and considered relations with various existing weak form of locally closed set. Preservations of direct images as well as inverse images of (.)*, ψ, *-perfect and various weak forms of locally closed set including *-Locally closed set are important investigating part. Besides, we pointed out that consideration of 'bijectivity' in Lemma 3.1 of [24] is sufficient, and the Lemma 3.3 of [24] is wrong. We demonstrated two modifications of the last one. [ABSTRACT FROM AUTHOR]

In this paper, in the line of Duman [7], we deal with Korovkin type approximation theory for a sequence of positive convolution operators defined on C[a,b], the Banach space of all real valued continuous functions on [a,b] endowed with the supremum norm || f || = supx∈[a,b] | f (x)| for f ∈ C[a,b], based on the notion of AI-summability. We construct an example to exhibit that the main result is more generalized than its statistical A-summable version. We also study the rate of AI-summability. [ABSTRACT FROM AUTHOR]

We solve the last standing open problem from the seminal paper by J. Gerlits and Zs. Nagy [Topology Appl. 14 (1982), pp. 151–161], which was later reposed by A. Miller, T. Orenshtein, and B. Tsaban. Namely, we show that under \mathfrak {p}=\mathfrak {c} there is a \delta-set that is not a \gamma-set. Thus we constructed a subset A of reals such that the space \mathrm {C}_p(A) of all real-valued continuous functions on A is not Fréchet–Urysohn, but possesses the Pytkeev property. Moreover, under \mathbf {CH} we construct a \pi-set that is not a \delta-set solving a problem by M. Sakai. In fact, we construct various examples of \delta-sets that are not \gamma-sets, satisfying finer properties parametrized by ideals on natural numbers. Finally, we distinguish ideal variants of the Fréchet–Urysohn property for many different Borel ideals in the realm of functional spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an equiprime fuzzy graph of a nearring with respect to the level ideal of a fuzzy ideal. We interrelate graph theoretical properties of the graph and ideal theoretical properties of nearring. We show that the properties like vertex cut, connectedness of the graph depend on the properties of the fuzzy ideal. We define ideal symmetry of the graph and find conditions for the graph to be ideal symmetric. If the fuzzy ideal is equiprime then we show that the level set induces a fuzzy clique. We find conditions required for the level set to be the vertex cover of the graph. We find interrelation between equiprime fuzzy graph and fuzzy graph of nearring with respect to level ideal. We study properties of the graph under neaaring homomorphism. We prove that the connectedness of the graph in homomorphic image depends on properties of ideal. We obtain conditions required for homomorphic image of an equiprime fuzzy ideal to be an equiprime fuzzy ideal. [ABSTRACT FROM AUTHOR]

This study aims to introduce the concept of α -ideal in bounded commutative residuated lattices and establish some related properties. In this paper, we show that the set of α -ideals of a bounded commutative residuated lattice is a Heyting algebra, and an algebraic lattice. Moreover, we state the prime α -ideal theorem, and describe relations between α -ideals and some types of ideals of a bounded commutative residuated lattice. Finally, we discuss correspondences between α -ideals and α -filters of a bounded commutative residuated lattice. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study the annihilating-ideal graph of an MV-algebra (A, ⊕, ∗, 0). The algebraic structure of MV-algebras (especially Boolean algebras) are described by using the annihilating-ideal graph. The connections between the ideal theory of MV-algebras and graph theory are established, which promote the studying of the coloring of graphs. The annihilating-ideal graph AG(A) is a simple graph with the vertex set V (AG(A)) = {I ∈ I(A)\{h0i, A} | ∃J ∈ I ∗ (A) such that IJ = h0i} and the edge set E(AG(A)) = {I − J | IJ = h0i, where I, J ∈ V (AG(A)) and I 6= J}, where I(A) is the set of all ideals of A and I ∗ (A) = I(A)\{h0i}. We verify that AG(A) is connected with dmax(AG(A)) ≤ 3. And we characterize some MV-algebras with dmax(AG(A)) = 0 or 1, where dmax(AG(A)) is the diameter of AG(A). If | A |≤ 7, we show that AG(A) is either a null graph, or dmax(AG(A)) = 1. We restrict MV-algebras to Boolean algebras. The connections between AG(A) and Γ(A) are studied, where Γ(A) is the zero-divisor graph of A. We characterize the complete graph AG(A) and the star graph AG(A) by using ann(A\{1}) = {a ∈ A | a ⊙ b = 0 for all b ∈ A\{1}}, where ann(A\{1}) is the annihilator of A\{1}. Finally, we study the vertex coloring and girth of AG(A). We give two lower bounds and an upper bound for χ(AG(A)). [ABSTRACT FROM AUTHOR]

Transaction fees are not simply a core source of revenue for payment service providers, but also impact significantly on the economy more broadly. This paper examines the situation in the Netherlands, where the banks in this relatively small country have historically cooperated to keep transaction costs low. With a focus on retail payments rather than the settlement of payment transactions or the payments leg of securities transactions, this paper explains the principles underlying this model of cooperation, and explores how cooperation within the payments industry has impacted the sector and country. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the structure of the variety of Lie algebras with a finite number of ideals and their graph representations using Hasse diagrams. The large number of necessary conditions on the algebraic structure of this type of algebras leads to the explicit description of those algebras in the variety with trivial Frattini subalgebra. To illustrate our results, we have included and discussed lots of examples throughout the paper. [ABSTRACT FROM AUTHOR]

In this paper, first the fuzzy set and i-(m,n)-near ring then fuzzy subgroups, fuzzy (m,n)-subnear ring and finally fuzzy ideals are defined. We state and prove theorems in these cases. Also in the next chapter, normal fuzzy subnear ring expressed and theorems about normal fuzzy subnear rings is expressed and proved. [ABSTRACT FROM AUTHOR]

AbstractLet V be a vector space and U a fixed subspace of V. We denote the semigroup of all linear transformations on V under composition of functions by L(V). In this paper, we study the semigroup of all linear transformations on V whose restrictions belong to the general linear group GL(U), denoted by LGL(U)(V). More precisely, we consider the subsemigroup LGL(U)(V)={α∈L(V):α|U∈GL(U)} of L(V). In this work, Green’s relations and ideals of this semigroup are described. Then we also determine the minimal ideal and the set of all minimal idempotents of it. Moreover, we establish an isomorphism theorem when V is a finite dimensional vector space over a finite field. Finally, we find its generating set. [ABSTRACT FROM AUTHOR]

In this paper, we extend the notion of IK convergence of sequence of real numbers to IK-st convergence by using the notion of K-statistical convergence. We investigate some of its properties and study its relation with some other known types of convergence. [ABSTRACT FROM AUTHOR]

This paper aims to examine the notion of λ-ideal statistical convergence and λ-ideal statistically Cauchy sequence over non-Archimedean 2-normed spaces. Moreover, we have also studied and proven some significant properties for λ-ideal statistically Cauchy sequence in 2-normed spaces to be λ-ideal statistically Cauchy with respect to II.II∞. And also we show that, λ-ideal statistical convergence in 2-normed spaces is λ-ideal statistical pre-Cauchy in 2-normed spaces over non-Archinedean field. Through this paper, K symbolizes a complete, non-trivially valued, non-Archinedean field. [ABSTRACT FROM AUTHOR]

As a continuation of the paper "Adjunction Identity to Hypersemigroup" in Turk J Math 2022; 46 (7): 2834-2853, it has been proved here that the adjunction of a greatest element to an ordered hypersemigroup is actually an embedding problem. The concept of pseudoideal has been introduced and has been proved that for each ordered hypersemigroup S an ordered hypersemigroup V having a greatest element (poe-hypersemigroup) can be constructed in such a way that there exists a pseudoideal T of S such that S is isomorphic to T. If S does not have a greatest element, then this can be regarded as the embedding of an ordered hypersemigroup in an ordered semigroup with greatest element. [ABSTRACT FROM AUTHOR]

Exponential algebra is a new algebraic structure consisting of a semigroup structure, a scalar multiplication, an internal multiplication and a partial order [introduced in [4]]. This structure is based on the structure 'exponential vector space' which is thoroughly developed by Priti Sharma et. al. in [11] [This structure was actually proposed by S. Ganguly et. al. in [1] with the name 'quasi-vector space'] Exponential algebra can be considered as an algebraic ordered extension of the concept of algebra. In the present paper we have shown that the function space C+(X) of all non-negative continuous functions on a topological space X is a topological exponential algebra under the compact open topology. Also we have discussed the ideals and maximal ideals of C+(X). We find an ideal of C+(X) which is not a maximal ideal in general; actually maximality of that ideal depends on the topology of X. The concept of ideals of exponential algebra was introduced by us in. [ABSTRACT FROM AUTHOR]

In this paper, using the concept of rough ideal convergence in normed linear spaces, we introduce rough ideal convergence for bounded linear operators. We also introduce some rough ideal convergent sequence spaces of bounded linear operators and further investigate and study some inclusion relations of these spaces, decomposition theorem and algebraic properties. [ABSTRACT FROM AUTHOR]

In this paper, we characterize when, for any infinite cardinal α , the Fremlin tensor product of two Archimedean Riesz spaces (see Fremlin in Am J Math 94:777–798, 1972) is Dedekind α -complete. We also provide an example of an ideal I in an Archimedean Riesz space E such that the Fremlin tensor product of I with itself is not an ideal in the Fremlin tensor product of E with itself. [ABSTRACT FROM AUTHOR]

Copyright of Methodological Horizons / Metodički Obzori is the property of Juraj Dobrila University of Pula and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The present paper aims to investigate the containment of nonzero central ideal in a ring R when the trace of symmetric n -derivations satisfies some differential identities. Lastly, we prove that in a prime ring R of suitable torsion restriction, if D , G : R n → R are two nonzero symmetric n -derivations such that f (ϑ) ϑ + ϑ g (ϑ) = 0 holds ∀ ϑ ∈ W , a nonzero left ideal of R where f and g are the traces of D and G , respectively, then either R is commutative or G acts as a left n -multiplier. Finally, we characterize symmetric n -derivations in terms of left n -multipliers. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Zhejiang University (Science Edition) is the property of Journal of Zhejiang University (Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This is from Birkhoff, the "father of lattice theory" in Trends in Lattice Theory. Van Nostrand 1970: "Lattices can do things for you, no matter what kind of mathematician you are!". The aim of this paper is to show that the le-semigroups (lattice ordered semigroups possessing a greatest element) play the main role in studying the ordered hypersemigroups. From many results on lattice ordered semigroups corresponding results on ordered semigroups can be obtained. The converse is also possible but the beauty and simplicity of "order" makes it easier to investigate the lattice ordered semigroup at first. After getting the results on ordered semigroups, by an easy modification corresponding results on ordered hypersemigroups can be obtained. [ABSTRACT FROM AUTHOR]

Let R be a non-commutative ring, and I be an ideal of R. In this paper, we generalize the definition of the zero-divisor graph of R with respect to I, and define several generalized zero-divisor graphs of R with respect to I. In this paper, we investigate the ring-theoretic properties of R and the graph-theoretic properties of all the generalized zero-divisor graphs. We study some basic properties of these generalized zero-divisor graphs related to the connectedness, the diameter and the girth. We also investigate some properties of these generalized zero-divisor graphs with respect to primal ideals. [ABSTRACT FROM AUTHOR]

In this paper, following the concept of AI-statistical convergence for real sequences introduced by Savas et al. [22], we deal with Korovkin type approximation theory for a sequence of positive convolution operators deĄned on C[a, b], the space of all real valued continuous functions on [a, b], in the line of Duman [6]. In the Section 3, we study the rate of AI-statistical convergence. [ABSTRACT FROM AUTHOR]