Search

In this paper, we study the ideal strong lacunary ward compactness of a subset of a 2-normed space and the ideal strongly lacunary ward continuity of a function on . Here a subset of is said to be ideal strong lacunary ward compact if any sequence in has an ideal strong lacunary quasi-Cauchy subsequence. Additionally, a function on is said to be ideal strong lacunary ward continuous if it preserves ideal strong lacunary quasi-Cauchy sequences; an ideal is defined to be a hereditary and additive family of subsets of . We find that a subset of with a countable Hamel basis is totally bounded if and only if it is ideal strong lacunary ward compact. [ABSTRACT FROM AUTHOR]

In this paper, we first construct a convex structure by ideals of effect algebras. Then we discuss convex properties of morphisms and monomorphisms between effect algebras. Further, we prove that partial binary operations ⊕ and ⊖ are separately convexity-preserving for the first position with respect to ideal convex structures when the effect algebra is a lattice effect algebra. A lattice effect algebra equipped with an ideal convex structure is called a semi-ideal convex effect algebra. Finally, we obtain that finite product and quotient of semi-ideal convex effect algebras are also semi-ideal convex effect algebras. [ABSTRACT FROM AUTHOR]

Let A be an MV-algebra. An (⊙ , ∨) -derivation on A is a map d : A → A satisfying: d (x ⊙ y) = (d (x) ⊙ y) ∨ (x ⊙ d (y)) for all x , y ∈ A . This paper initiates the study of (⊙ , ∨) -derivations on MV-algebras. Several families of (⊙ , ∨) -derivations on an MV-algebra are explicitly constructed to give realizations of the underlying lattice of an MV-algebra as lattices of (⊙ , ∨) -derivations. Furthermore, (⊙ , ∨) -derivations on a finite MV-chain are enumerated and the underlying lattice is described. [ABSTRACT FROM AUTHOR]

In a large number of multivalued logic and fuzzy logic of algebraic systems, residuated lattices play a prominent role and have considerable applications. States operators have been introduced on residuated lattices, and their properties are useful for the development of an algebraic theory of probabilistic models of those algebras. In this paper, we introduce the notion of state ideal in the framework of state residuated lattices, investigate some related properties, and provide several examples. Also, we present two types of state residuated lattices: state i-simple residuated lattices and state i-local residuated lattices, and characterize them. Moreover, the relationship between state ideals and state filters is analyzed using the set of complement elements. Furthermore, we prove that the lattice of all state ideals of a given state residuated lattice is a complete lattice. The notion of obstinate state ideals in state residuated lattices is also introduced, and several characterizations are presented. [ABSTRACT FROM AUTHOR]

In this paper, a new diamond–silicon carbide ceramic composite material—Ideal—is studied and its mechanical characteristics are determined. For the first time, a comprehensive determination of Poisson's ratio, shear modulus, bulk modulus, and transverse sound velocity is carried out. Poisson's ratio is in the region of 0.008 to 0.01, which, in turn, indicates the absolutely brittle nature of the failure of the Ideal ceramic under loading. The criteria that allow evaluating different materials used for body armor are calculated. [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]

In this paper we describe commutative monoids S containing a zero element in which every ideal is the annihilator of an element of S. [ABSTRACT FROM AUTHOR]

Let C n denote the order-preserving and decreasing full transformation semigroup on X n = { 1 , 2 , ... , n } . In this paper, first we describe each principal ideal of C n . Second, we discuss left and right abundance of the principal ideals of C n . Further, necessary and sufficient conditions for the principal ideals in C n to be abundant and regular are given. Finally, we study abundance of the ideals in C n . [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]

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]

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]

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 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 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]

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 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, we define the notion of uniform BL-algebras and derive some conditions under which the operations of BL-algebras are uniformly continuous. Also, some properties of uniform topology are discussed. Finally, we use some types of congruence relations to construct some uniformities and analyze the relationship between these uniformities. [ABSTRACT FROM AUTHOR]

Let t ≥ 2 be an integer, and let p1, ⋯, pt be distinct primes. By using algebraic properties, the present paper gives a sufficient and necessary condition for the existence of non-trivial self-orthogonal cyclic codes over the ring Z p 1 p 2 ⋯ p t and the corresponding explicit enumerating formula. And it proves that there does not exist any self-dual cyclic code over Z p 1 p 2 ⋯ p t . [ABSTRACT FROM AUTHOR]

This paper considers the problem of constructing reduced disjunctive normal forms of order-convex Boolean functions. An original algorithm is proposed for finding these forms. The algorithm uses concepts of the theory of ordered sets such as an ideal and a coideal and has a substantially lower time complexity than the classical Quine-McCluskey algorithm. [ABSTRACT FROM AUTHOR]

We say that an ideal ℐ has property (T) if for every ℐ-convergent series ∑n=1∞xn, there exists a set A ∈ ℐ such that ∑n ∈ ℕ\Axn converges in the usual sense. The main aim of this paper is to focus on several different classes of ideals, such as summable ideals, Fσ ideals, and matrix summability ideals, and to show that they do not have the mentioned property. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the study of some subclasses of H-rings, i.e., rings in which all subrings are ideals. In the description of H-rings an important role is played by almost null rings. We classify, up to isomorphism, torsion almost null rings of bounded exponent. [ABSTRACT FROM AUTHOR]

We say that an ideal $${\mathcal{I}}$$ on $${\omega}$$ is homogeneous, if its restriction to any $${\mathcal{I}}$$ -positive subset of $${\omega}$$ is isomorphic to $${\mathcal{I}}$$ . The paper investigates basic properties of this notion - we give examples of homogeneous ideals and present some applications to topology and ideal convergence. Moreover, we answer questions related to our research posed in [1]. [ABSTRACT FROM AUTHOR]

In this paper we show that if I is an ideal of a commutative semigroup C such that the separator SepI of I is not empty then the factor semigroup $$S=C/P_I$$ ( $$P_I$$ is the main congruence of C defined by I) satisfies Condition $$(*)$$ : S is a commutative monoid with a zero; The annihilator A( s) of every non identity element s of S contains a non zero element of S; $$A(s)=A(t)$$ implies $$s=t$$ for every $$s, t\in S$$ . Conversely, if $$\alpha $$ is a congruence on a commutative semigroup C such that the factor semigroup $$S=C/\alpha $$ satisfies Condition $$(*)$$ then there is an ideal I of C such that $$\alpha =P_I$$ . Using this result for the multiplicative semigroup $$D_{mult}$$ of a unique factorization domain D, we show that $$P_{J(m)}=\tau _m$$ for every nonzero element $$m\in D$$ , where J( m) denotes the ideal of D generated by m, and $$\tau _m$$ is the relation on D defined by $$(a, b)\in \tau _m$$ if and only if $$gcd(a, m)\sim gcd(b, m)$$ ( $$\sim $$ is the associate congruence on $$D_{mult}$$ ). We also show that if a is a nonzero element of a unique factorization domain D then $$d(a)=|D'/P_{J([a])}|$$ , where d( a) denotes the number of all non associated divisors of a, $$D'=D/\sim $$ , and [ a] denotes the $$\sim $$ -class of $$D_{mult}$$ containing a. As an other application, we show that if d is one of the integers $$-1$$ , $$-2$$ , $$-3$$ , $$-7$$ , $$-11$$ , $$-19$$ , $$-43$$ , $$-67$$ , $$-163$$ then, for every nonzero ideal I of the ring R of all algebraic integers of an imaginary quadratic number field $${\mathbb Q}[\sqrt{d}]$$ , there is a nonzero element m of R such that $$P_I=\tau _m$$ . [ABSTRACT FROM AUTHOR]

Let R be a *-prime ring with center Z(R), d a non-zero (σ,τ)- derivation of R with associated automorphisms σ and τ of R, such that σ,τ and d commute with '*'. Suppose that U is an ideal of R such that U* = U, and Cσ,τ = {c ∈ R | cσ(x) = τ(x)c for all x ∈ R}. In the present paper, it is shown that if characteristic of R is different from two and [d(U); d(U)]σ,τ = {0}, then R is commutative. Commutativity of R has also been established in case if [d(R),d(R)]σ,τ ⊆ Cσ,τ. [ABSTRACT FROM AUTHOR]

This paper is primarily concerned with a natural extension of the notion of a total graph $$T(\varGamma (R))$$ in the realm of signed graph for a finite commutative ring R. First, we characterize the rings for which the signed total graph $$T_{\varSigma }(\varGamma (R))$$ and its line signed graph $$L(T_{\varSigma }(\varGamma (R)))$$ are balanced. Second, we characterize the rings for which the negation of a signed total graph $$\eta (T_{\varSigma }(\varGamma (R)))$$ is balanced. Several new directions for further research are also indicated. [ABSTRACT FROM AUTHOR]

The rough approximations on a complete completely distributive lattice L based on binary relation were introduced by Zhou and Hu (Inf Sci 269:378-387, 2014), where the binary relation was defined on the set of non-zero join-irreducible elements. This paper extends Zhou and Hu's rough set model by defining new approximation operators via ideal. When I is the least ideal of L and R is a reflexive binary relation, these two approximations coincide. We present the essential properties of new approximations and also discuss how the new one relates to the old one. Finally, the topological and lattice structures of the approximations are given. [ABSTRACT FROM AUTHOR]

We generalize the notions of strongly dominating and strongly unbounded subset of the Baire space. We compare the corresponding ideals and tree ideals, in particular we present a condition which implies that some of those ideals are distinct. We also introduce $${\mathrm{DU}_\mathcal{I}}$$ -property, where $${\mathcal{I}}$$ is an ideal on cardinal $${\kappa}$$ , to capture these two generalized notions at once. We use two player game defined in a Kechris's paper (Trans Am Math Soc 229:191-207, ) to show that every $${\lambda}$$ -Suslin set with $${\mathrm{DU}_\mathcal{I}}$$ -property contains a perfect subset with $${\mathrm{DU}_\mathcal{I}}$$ -property, provided that $${\lambda}$$ is sufficiently small. [ABSTRACT FROM AUTHOR]

In the paper, (congruence-simple) semirings with at least two left multiplicatively absorbing elements are investigated. Main emphasis is laid on semirings of type (A) which generalize the endomorphism semirings of semilattices. [ABSTRACT FROM AUTHOR]

Le Riche, Meldrum and Van der Walt introduced the concept of a group near-ring. Thereafter, starting with an ideal in the base near-ring, they constructed two corresponding ideals in the group near-ring. Furthermore, by starting with an ideal in the group near-ring, they constructed a corresponding ideal in the base near-ring. In this we paper, we generalise both the concept of the group near-ring and the construction of the three ideals. We introduce a fourth ideal, and we investigate some relationships amongst these four ideals. We also investigate whether a prime condition placed on an R-ideal of a near-ring module implies that prime condition on the corresponding ideal in the generalised group near-ring and vice versa. [ABSTRACT FROM AUTHOR]

In this paper we discuss prime down-sets of a semilattice. We give a characterization of prime down-sets of a semilattice. We also give some characterizations of 0-distributive semilattices and a characterization of minimal prime ideals containing an ideal of a 0-distributive semilattice. Finally, we give a characterization of minimal prime ideals of a pseudocomplemented semilattice. [ABSTRACT FROM AUTHOR]

In this paper, following a very recent and new approach, we further generalize recently introduced summability methods, namely, I-statistical convergence and I-lacunary statistical convergence (which extend the important summability methods, statistical convergence and lacunary statistical convergence using ideals of N) and introduce the notions of I-statistical convergence of order α and I-lacunary statistical convergence of order α, where 0 < α < 1. We mainly investigate their relationship and also make some observations about these classes and in the way try to give an answer to an open problem posed By Das, Savas and Ghosal in 2011. The study leaves a lot of interesting open problems. [ABSTRACT FROM AUTHOR]

It is well known that being an ideal (left ideal, right ideal) of a ring is not a transitive relation. Nevertheless in some cases the transitive property does hold. Systematic studies of this subject were started in [11,13]. In this paper we continue these studies. [ABSTRACT FROM AUTHOR]

MV-algebras as well as orthomodular lattices can be seen as a particular case of so-called 'basic algebras' which are an alter ego of bounded lattices whose sections are equipped with fixed antitone involutions. The class of basic algebras is an ideal variety. In the paper, we give an internal characterization of congruence kernels (ideals) and find a finite basis of ideal terms, with focus on monotone and effect basic algebras. We also axiomatize basic algebras that are subdirect products of linearly ordered ones. [ABSTRACT FROM AUTHOR]

The notion of rough sets was introduced by Z. Pawlak in 1982. The concept of G-semihyperring is a generalization of semihyperring, Γ-semiring and semiring. In this paper, we study the notion of a rough (rough prime) ideal in a Γ-semihyperring. Also, we discuss the relation between the upper and lower rough ideals and the upper and lower approximation of their homomorphism images. [ABSTRACT FROM AUTHOR]

Basic algebras are a generalization of MV-algebras, also including orthomodular lattices and lattice effect algebras. A pre-ideal of a basic algebra is a non-empty subset that is closed under the addition ⊕ and downwards closed with respect to the underlying order. In this paper, we study the pre-ideal lattices of algebras in a particular subclass of basic algebras which are closer to MV-algebras than basic algebras in general. We also prove that finite members of this subclass are exactly finite MV-algebras. [ABSTRACT FROM AUTHOR]

In this paper, we consider both algebraic crossed products of commutative complex algebras A with the integers under an automorphism of A, and Banach algebra crossed products of commutative C*-algebras A with the integers under an automorphism of A. We investigate, in particular, connections between algebraic properties of these crossed products and topological properties of naturally associated dynamical systems. For example, we draw conclusions about the ideal structure of the crossed product by investigating the dynamics of such a system. To begin with, we recall results in this direction in the context of an algebraic crossed product and give simplified proofs of generalizations of some of these results. We also investigate new questions, for example about ideal intersection properties of algebras properly between the coefficient algebra A and its commutant A′. Furthermore, we introduce a Banach algebra crossed product and study the relation between the structure of this algebra and the topological dynamics of a naturally associated system. [ABSTRACT FROM AUTHOR]

Denote by Mat k,l( F) the algebra M n( F) of matrices of order n = k + l with the grading (Mat( F),Mat( F)), where Mat( F) admits the basis and Mat( F) admits the basis . Denote by M k,l( F) the Grassmann envelope of the superalgebra Mat k,l( F). In the paper, bases of the graded identities of the superalgebras Mat1,2( F) and M1,2( F) are described. [ABSTRACT FROM AUTHOR]

The segregated algorithm-IDEAL (inner doubly-iterative efficient algorithm for linked-equations) is an efficient and stable algorithm. In this algorithm, there exist inner doubly-iterative processes for pressure equation, which almost completely overcome two approximations in SIMPLE algorithm. Thus the coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of iteration process. In this paper, implementation of the IDEAL algorithm on a 3D collocated grid system is conducted. The interlace velocity is calculated by the modified momentum interpolation method (MMIM), by which the converged result is independent of the under-relaxation factor. Finally, five three-dimensional incompressible fluid flow and heat transfer problems are provided to compare the convergence rate and robustness between the IDEAL and three other most widely-used algorithms (SIMPLER, SIMPLEC and PISO). By the comparison it can be concluded that the IDEAL algorithm is more robust and efficient than the three other algorithms. [ABSTRACT FROM AUTHOR]

The main result of the paper is a structure theorem concerning the ideal extensions of archimedean ordered semigroups. We prove that an archimedean ordered semigroup which contains an idempotent is an ideal extension of a simple ordered semigroup containing an idempotent by a nil ordered semigroup. Conversely, if an ordered semigroup S is an ideal extension of a simple ordered semigroup by a nil ordered semigroup, then S is archimedean. As a consequence, an ordered semigroup is archimedean and contains an idempotent if and only if it is an ideal extension of a simple ordered semigroup containing an idempotent by a nil ordered semigroup. [ABSTRACT FROM AUTHOR]

Stone-Čech compactifications derived from a discrete semigroup S can be considered as the spectrum of the algebra ℬ( S) or as a collection of ultrafilters on S. What is certain and indisputable is the fact that filters play an important role in the study of Stone-Čech compactifications derived from a discrete semigroup. It seems that filters can play a role in the study of general semigroup compactifications too. In the present paper, first we review the characterizations of semigroup compactifications in terms of filters and then extend some of the results in Papazyan (Semigroup Forum 41:329–338, ) concerning the Stone-Čech compactification to a semigroup compactification associated with a Hausdorff semitopological semigroup. [ABSTRACT FROM AUTHOR]

In this paper, the semigroup of primitive generalized circulant Boolean matrices is studied, and some algebraic properties of this semigroup are obtained. Also, an asymptotic formula for the cardinality of the semigroup is given. [ABSTRACT FROM AUTHOR]

In the paper, the notions of radical of an ideal and radical of a submodule are generalized and described. [ABSTRACT FROM AUTHOR]

This paper characterizes ideal structure of the uniform Roe algebra B*(X) over simple cores X. A necessary and sufficient condition for a principal ideal of B*(X) to be spatial is given and an example of non-spatial ideal of B*(X) is constructed. By establishing an one-one correspondence between the ideals of B*(X) and the ω-filters on X, the maximal ideals of B*(X) are completely described by the corona of the Stone-Čech compactification of X. [ABSTRACT FROM AUTHOR]

Vanishing component analysis (VCA) method, as an important method integrating commutative algebra with machine learning, utilizes the polynomial of vanishing component to extract the features of manifold, and solves the classification problem in ideal space dual to kernel space. But there are two problems existing in the VCA method: first, it is difficult to set a threshold of its classification decision function. Second, it is hard to handle with the over-scaled training set and oversized dimension of eigenvector. To address these two problems, this paper improved the VCA method and presented a grouped VCA (GVCA) method by grouping strategy. The classification decision function did not use a predetermined threshold; instead, it solved the values of all polynomials of vanishing component and sorted them, and then used majority voting approach to determine their classes. After that, a strategy of grouping training set was proposed to segment training sets into multiple non-intersecting subsets, which polynomials of vanishing component were later acquired through a VCA method, respectively, and finally combined into an integral set of vanishing component polynomial. What is more important is that it uses the bagging theory in ensemble learning to successfully expound and prove the correctness of the strategy of grouping training sets. It also compares the time complexity for training algorithm with and without grouping training sets, thus demonstrating the effectiveness of the grouping strategy. A series of experiments showed that the GVCA method proposed in the paper has a perfect classification performance with a rapid rate of convergence compared to other statistical learning methods. [ABSTRACT FROM AUTHOR]