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In this paper, we have introduced neutrosophic hyperideals of a semihyperring and considered some operations on them to study its basic notions and properties. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of a disjoint union of pseudo-BCH-algebras and describe ideals in such algebras. We also investigate ideals of direct products of pseudo-BCH-algebras. Moreover, we establish conditions for the set of all minimal elements of a pseudo-BCH-algebra χ to be an ideal of χ. [ABSTRACT FROM AUTHOR]

This paper aims to apply fuzzy sets and soft sets in combination to investigate algebraic properties of regular AG-groupoids. We initiate (∊γ, ∊γ; V-qδ)-fuzzy soft left ideals (right ideals, bi-ideals and quasi-ideals) over AG-groupoids and explore some related properties. Moreover, we give a number of characterizations for regular AG-groupoids by virtue of various types of fuzzy soft ideals over them. [ABSTRACT FROM AUTHOR]

The concept of statistical convergence is one of the most active area of research in the field of summability. Over the years and under different names statistical convergence has been discussed in the theory of Fourier analysis, ergodic theory and number theory. In this paper, we introduce the idea of double Jλ -statistical convergence in a locally solid Riesz space and study some of its properties by using the mathematical tools of the theory of topological vector spaces. [ABSTRACT FROM AUTHOR]

In this paper we have introduced some classes of new sequence spaces ... of fuzzy numbers using the notion of rough I-convergence. We study some basic topological and algebraic properties of these spaces. We also investigate some inclusion relations related to these spaces. [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 this paper we consider the notion of 2I-statistical convergence for real double sequences which is an extension of the notion of 2I-statistical convergence for real single sequences introduced by Savas, Das and Dutta. We primarily apply this new notion to prove a Korovkin type approximation theorem. In the last section, we study the rate of 2I-statistical convergence. [ABSTRACT FROM AUTHOR]

In this paper we first consider the ideas of weak statistical and ideal convergence in a normed linear space and present a characterization. It should be noted that the characterization has earlier been proved in [4], but there are faults in the arguments. We present the correct argument partially. We also introduce the ideas of weak I and I* - divergences following [7] and make certain observations. [ABSTRACT FROM AUTHOR]

In this paper, we prove that (X, τ) and the new topology (X, τε) have the same semiregularization if ε is a π-network in X with the property H. Also, we discuss the properties of ε, τε and study generalized Volterra spaces and discuss their properties. We show that τε coincides with the ⋆-topology for a particular ε. [ABSTRACT FROM AUTHOR]

The Tamari lattice of order n can be defined on the set T n of binary trees endowed with the partial order relation induced by the well-known rotation transformation. In this paper, we restrict our attention to the subset M n of Motzkin trees. This set appears as a filter of the Tamari lattice. We prove that its diameter is 2 n − 5 and that its radius is n − 2 . Enumeration results are given for join and meet irreducible elements, minimal elements and coverings. The set M n endowed with an order relation based on a restricted rotation is then isomorphic to a ranked join-semilattice recently defined in Baril and Pallo (2014). As a consequence, we deduce an upper bound for the rotation distance between two Motzkin trees in T n which gives the exact value for some specific pairs of Motzkin trees. [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]

In this paper we introduce I2-statistical convergence and I2-statistical Cauchy of double sequences in 2-normed spaces and investigate their relationship. [ABSTRACT FROM AUTHOR]

In this paper, we present an unified approach which defines interval valued L-fuzzy ideals of nearrings by incorporating interval valued t-norms and t-conorms. We characterize interval valued L-fuzzy ideals in terms of their level subsets. We study insertion of factors property and relate interval valued fuzzy points with interval valued fuzzy ideals. [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 consider a class of special subsets of a BCK-algebra and investigate some related properties. We describe the intersection and union of two of these subsets in a commutative BCK-lattice. We consider the intersection of all special subsets in a BCK-algebra and investigate some related properties. Finally, we introduce the connection between the class of special subsets and the set of all congruence classes induced by an ideal in a BCK-algebra. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new notions, namely, ideal statistical convergence and ideal lacunary statistical convergence for fuzzy numbers, their relationship and also make some observations about these classes. [ABSTRACT FROM AUTHOR]

In this paper, we study the ideal incompressible density-dependent Oldroyd model in ℝn(n = 2, 3). We establish local in time existence and uniqueness of solutions for the ideal incompressible density-dependent Oldroyd model. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of symmetric bi-multiderivations on incline algebras and investigate some properties of the notion. [ABSTRACT FROM AUTHOR]

An ideal I is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. In this paper we introduce ideal convergent sequence spaces of fuzzy numbers using σ-bounded variation and Orlicz functions and study some basic topological and algebraic properties of these spaces. Finally we investigate the inclusions relations related to these spaces. [ABSTRACT FROM AUTHOR]

A convolution is a mapping C of the set (ℱ+ of positive integers into the set P ((ℱ+) of all subsets of (ℱ+ such that, for any n ϵ (ℱ+ , each member of C(n) is a divisor of n. If D(n) is the set of all divisors of n, for any n, then D is called the Dirichlet's convolution. Corresponding to any general convolution C, we can define a binary relation ≤C on (ℱ+ by "m (≤C n if and only if m ϵ C(n)". It is well known that (ℱ+ has the structure of a distributive lattice with respect to the division order. The division ordering is precisely the partial ordering =D induced by the Dirichlet's convolution D. In this paper, we present a characterization for the prime ideals in ((ℱ+,≤D) , where D is the Dirichlet's convolution. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of $\mathcal{I}$-statistical convergence and $\mathcal{I}$-lacunary statistical convergence with respect to the intuitionistic fuzzy norm $\left( \mu,v\right) $, investigate their relationship, and make some observations about these classes. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two different stabilizers of X with respect to Y for subsets X and Y of an MV-algebra A. We show that stabilizers are ideals and we investigate the relation between stabilizers and some other ideals in MV-algebras. We also show that if I and J are ideals in an MV-algebra A, then the stabilizer of I with respect to J is the relative pseudo-complement of I with respect to J in the lattice of ideals of A. [ABSTRACT FROM AUTHOR]

Let A be a Banach algebra and X be a Banach A-bimodule. In this paper, we de ne a new product on A ⊕ X and generalize the module extension Banach algebras. We obtain characterizations of Arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new Banach algebra. [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]

This article is motivated by the recent paper "Characterization of the ideal core" by Paolo Leonetti (JMAA, 2019). We show that in the main result of that paper the first countability condition can be omitted, and the compactness condition may be substituted by a strictly weaker one. [ABSTRACT FROM AUTHOR]

The partial functions under disjoint-domain sums and functional composition do not form a field, and thus conventional linear algebra is not applicable. However they can be regarded as a so-ring, an algebraic structure possessing a natural partial ordering, an infinitary partial addition and a binary multiplication, subject to a set of axioms. In this paper, we introduce the notions of 2-absorbing ideal of so-rings and 2-absorbing subsemimodule of partial semimodules and study their characteristics. [ABSTRACT FROM AUTHOR]

In this paper we first calculate the number of vertices and edges of the intersection graph of ideals of direct product of rings and fields. Then we study Eulerianity and Hamiltonicity in the intersection graph of ideals of direct product of commutative rings. [ABSTRACT FROM AUTHOR]

he paper analyzes the methodological approach of the Bulgarian philosopher Assen Ignatow toward the reality of socialist society in his book „Grief and Urge of Time“ (1968). The dichotomy between the ideal and the actual practice in society, between the Marxist philosophy and the dogmatic communist ideology, between the ideal man and the real man is emphasized. The differences and the continuities between philosophical ideas, developed in this book and in later important works of Ignatow, are analyzed. [ABSTRACT FROM AUTHOR]

In this paper we introduce some new double sequence spaces of fuzzy real numbers by combining I-convergence, Orlicz function and four dimensional matrix and we examine some properties of the resulting sequences spaces of fuzzy numbers. [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]

In this paper we extend the notion of equal convergence of Császár and Laczkovich with the help of ideals of the set of positive integers and introduce the ideas of I and I*-equal convergence and prove certain properties. Throughout the investigation two classes of ideals, one satisfying "Chain Condition" and another called P-ideals play a very important role. We also introduce certain related notions of convergence and prove an Egoroff-type theorem for I*-equal convergence. [ABSTRACT FROM AUTHOR]

An ideal I is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. In this paper we have introduced ideal convergent sequences of fuzzy real numbers using σ-uniform density. Furthermore, inclusion between Iσ-convergence and invariant convergence also Iσ-convergence and $[V_{\sigma}]^{F}_p$-convergence were given. [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]

In this paper, we define new classes of sets called preopen sets, θI-semi-open sets, θI-β-open sets and θI-α-open sets in ideal topological spaces. Also, by using these sets, we obtain new decompositions of continuity in ideal topological spaces. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the problem of embedding of filial ring into filial ring with an identity. [ABSTRACT FROM AUTHOR]

In this paper, we defined Weak ideal of a C-algebra and proved certain important properties of Weak ideals. It is proved that Weak ideals of any C-algebra form an algebraic lattice whenever the C-algebra possesses smallest element with respect to the partial order induced by *. [ABSTRACT FROM AUTHOR]

In this paper, we consider a collection of deductive systems of a distributive implication groupoid X. We use the concept of congruence relation with respect to deductive systems to construct a uniformity that induces a topology on X which makes this to a topological distributive implication groupoids. [ABSTRACT FROM AUTHOR]

In the paper there are investigated some properties of Lie algebras, the construction which has a wide range of applications like computer sciences (especially to computer visions), geometry or physics, for example. We concentrate on the semidirect sum of algebras and there are extended some theoretic designs as conditions to be a center, a homomorphism or a derivative. The Killing form of the semidirect sum where the second component is an ideal of the first one is considered as well. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we primarily consider the notion of -covers recently introduced in [11] as well as related notion of -covers [9] and make some further investigations. In particular we consider the notion of κ-covers studied by Di Maio, Kočinac, Meccariello and Caserta in [8,18], and establish some results involving -covers ( -covers) and κ-covers. Our results extend the earlier results proved in [6,8,18,29] and present a more general version using the notion of ideals. [Copyright &y& Elsevier]

The aim of this paper is to give a classification theorem for commutative torsion filial rings. [ABSTRACT FROM AUTHOR]

The legal configuration of kinship ties in immigration law is governed by a restrictive logic that combines a dependent and nuclear composition with mismatches in the concrete form of managing the distances, the dynamics and the times at origin and destination. The family model in immigration law has an ideal and dominant approach openly excluding other family realities in the social context. Law in an inherent tendency towards the ideal doesn't allow a legitimate choice between autonomy and individual freedom in order to define or not the family project and own relationships. In this paper I discuss from a critical approach the inconsistencies presented by the current Spanish immigration law to restructure households in the family reunification scheme because of Law doesn't secure a suitable degree of equality and justice. [ABSTRACT FROM AUTHOR]

Let L be a completely regular frame and, as customary, let R L denote the ring of continuous real-valued functions on L. In the first part of the paper we characterize the maximal regular ideal of R L. We show that it consists precisely of the functions α such that the open sublocale of L associated with coz α is clopen and is a P -frame. We also give a characterization of this ideal in terms of the notion of the localic remainder. In contrast, the maximal regular ideal of the ring Z L of continuous integer-valued functions on L is shown to be always the zero ideal. Purity and regularity of ideals are germane in the description and characterization of the maximal regular ideal of R L. It is for this reason that in the last part of the paper we consider ideals of ideals of R L because, as we prove, it is precisely the pure ideals of R L all of whose ideals are ideals in the whole ring. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce the generalized ideal based zero divisor graph of a poset , denoted by . A representation theorem is obtained for generalized zero divisor graphs. It is proved that a graph is complete -partite with if and only if it is a generalized zero divisor graph of a poset. As a consequence of this result, we prove a form of a Beck’s Conjecture for generalized zero divisor graphs of a poset. Further, it is proved that a generalized zero divisor graph of a section semi-complemented poset with respect to the ideal is a complete graph. [Copyright &y& Elsevier]

Abstract: Let be a probability measure on a separable Banach space . A subset is -continuous if . In the paper the -continuity and uniform -continuity of convex bodies in , especially of balls and half-spaces, is considered. The -continuity is interesting for study of the Glivenko–Cantelli theorem in Banach spaces. Answer to a question of F. Topsøe is given. [Copyright &y& Elsevier]

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]

In this paper, we consider a collection of ideals of a KK-algebra X. We use the concept of congruence relation with respect to ideals to construct a uniformity that induces a topology on X which makes this to a topological KK-algebras. [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]

Abstract: In this paper we make some further investigations on ideal convergence and in particular we concentrate on -limit points and -cluster points. We try to establish the characterization of the set of -limit points (which has not been done in any structure so far) and show that this set can be characterized as an -set for a large class of ideals, namely analytic P-ideals and then make certain interesting observations on -cluster points. [Copyright &y& Elsevier]

The notion of Fuzzy BF-subalgebras was developed by A. Borumand Saeid and M. A. Rezvani in 2009. Recently, in 2010, we introduced the notion of Intuitionistic L-fuzzy ideals and in 2011 the notion of Intuitionistic L-fuzzy H-ideal of BF-algebras. This paper deals with the idea of Intuitionistic L-fuzzy p-ideal of a BF-algebra and some results on it. [ABSTRACT FROM AUTHOR]

In this paper, using the difference operator of order m, the sequences of Orlicz functions and double lacunary sequence we introduce and study some classes of sequences of fuzzy numbers defined by I-convergence. We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces. [ABSTRACT FROM AUTHOR]