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In this paper, we first introduce the notions of pseudo symmetric subset and pseudo symmetric ideal of a near-ring and define pseudo symmetric near-ring. We prove that every completely prime (resp. completely semiprime) ideal of a near-ring is a pseudo symmetric ideal. We also show that a near-ring satisfying the strong insertion factor property (resp. the weak commutative near-ring ) is a pseudo sym- metric near-ring. Moreover, we investigate the relations among the radicals of type 1 prime, pseudo symmetric, completely prime, com- pletely semiprime, primary and semiprimary ideals of a near-ring [ABSTRACT FROM AUTHOR]

The Tutte polynomial was originally a bivariate polynomial enumerating the colorings of a graph and of its dual graph. But it reveals more of the internal structure of the graph like its number of forests, of spanning subgraphs, and of acyclic orientations. In 2007, Ardila extended the notion of Tutte polynomial to hyperplane arrangements, and computed the Tutte polynomials of the classical root systems for certain prime powers of the first variable at the same time. In this paper, we compute the Tutte polynomial of ideal arrangements. These arrangements were introduced in 2006 by Sommers and Tymoczko, and are defined for ideals of root systems. For the ideals of classical root systems, we bring a slight improvement of the finite field method by showing that it can applied on any finite field whose cardinality is not a minor of the matrix associated to the studied hyperplane arrangement. Computing the minor set associated to an ideal of classical root systems particularly permits us to deduce the Tutte polynomials of the classical root systems. For the ideals of the exceptional root systems of type G 2 , F 4 , and E 6 , we use the formula of Crapo. [ABSTRACT FROM AUTHOR]

As pointed out in the monographs [5, 6] on semirings, ideals play an important role despite the fact that they need not be congruence kernels as in the case of rings. Hence, having two commutative semirings S1 and S2, one can ask whether an ideal I of their direct product S = S1 ×S2 can be expressed in the form I1 ×I2 where Ij is an ideal of Sj for j = 1,2. Of course, the converse is elementary, namely if Ij is an ideal of Sj for j = 1,2 then I1 × I2 is an ideal of S1 × S2. Having a congruence Θ on a commutative semiring S, its 0-class is an ideal of S, but not every ideal is of this form. Hence, the lattice IdS of all ideals of S and the lattice KerS of all congruence kernels (i.e. 0-classes of congruences) of S need not be equal. Furthermore, we show that the mapping Θ 7→ [0]Θ need not be a homomorphism from ConS onto KerS. Moreover, the question arises when a congruence kernel of the direct product S1 ×S2 of two commutative semirings can be expressed as a direct product of the corresponding kernels on the factors. In the paper we present necessary and sufficient conditions for such direct decompositions both for ideals and for congruence kernels of commutative semirings. We also provide sufficient conditions for varieties of commutative semirings to have directly decomposable kernels. [ABSTRACT FROM AUTHOR]

In this paper, the concepts of J2 -Cauchy. J2* -Cauchy double sequences in fuzzy n-normed spaces were introduced and some properties and relations of them were studied. We show that if a double sequence (xmr) in X is an 3-double Cauchy sequence, then it is J2*-double Cauchy sequence, where J, denotes the ideal of subsets of NxN. [ABSTRACT FROM AUTHOR]

In this paper, we consider the notion of AI-statistical convergence for real sequences and establish a Korovkin type approximation theorem for positive linear operators on UC*[0;1), the Banach space of all real valued uniform continuous functions on [0;∞) with the property that limx!∞ f(x) exists finitely for any f 2 UC*[0;∞). We then construct an example which shows that our new result is stronger than its classical version. In the section 3, we extend the Korovkin type approximation theorem for positive linear operators on UC*([0;∞) × [0;∞)). [ABSTRACT FROM AUTHOR]

In this paper, we consider the notion of I-equal convergence introduced by Das, Dutta, and Pal [9], and two related notions of convergence, namely, I-discrete, and I -strong uniform equal convergence and primarily investigate some lattice properties of the corresponding Baire classes obtained from a class of functions $. [ABSTRACT FROM AUTHOR]

In this paper, we generalize previous studies on right ideals of prime ring 𝑅 with generalized 𝛼 - derivation 𝐷 and show that 𝑅 is commutative under different conditions. Also, we investigate commutative property of prime ring 𝑅 for two generalized 𝛼 - derivations 𝐷 and 𝐻. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of n -fold boolean ideals, n -fold implicative ideals and n -fold integral ideals in residuated lattices and we state and prove their properties. Several characterizations of these notions are derived and the relations between those notions are investigated. Also, we construct the correspondence between the notions of n -fold ideal and n -fold filter in residuated lattices. [ABSTRACT FROM AUTHOR]

The paper deals with an algebraic extension of MV-algebras based on the definition of generalized Boolean algebras. We introduce a new class of structures, not necessarily with a top element, which are called EMV-algebras, in a way that every EMV-algebra contains an MV-algebra. First, we present basic properties of EMV-algebras. We give some examples, introduce and investigate congruence relations, ideals and filters on these algebras. We establish a basic representation result saying that each EMV-algebra can be embedded into an EMV-algebra with top element and we characterize EMV-algebras either as structures which are termwise equivalent to MV-algebras or as maximal ideals of EMV-algebras with top element. We study the lattice of ideals of an EMV-algebra and prove that every EMV-algebra has at least one maximal ideal. We define an EMV-clan of fuzzy sets as a special EMV-algebra where all operations are defined by points. We show that any semisimple EMV-algebra is isomorphic to an EMV-clan of fuzzy functions on a set. The set of EMV-algebras is neither a variety nor a quasivariety, but rather a special class of EMV-algebras which we call a q-variety of EMV-algebras. We present an equational base for each proper q-subvariety of the q-variety of EMV-algebras. We establish categorical equivalencies among the category of proper EMV-algebras, the category of MV-algebras with a fixed special maximal ideal, and a special category of Abelian unital ℓ -groups. [ABSTRACT FROM AUTHOR]

Let R be a prime ring with involution ⋆, and let σ, τ be endomorphisms on R. For any x , y ∈ R, let (x, y)σ, τ = xσ (y) + τ(y)x and Cσ, τ(R) = {x ∈ R∣ xσ(y) = τ(y)x. An additive subgroup U of R is said to be a (σ, τ)-right Jordan ideal (resp. (σ, τ-left Jordan ideal) of R if (U, R)σ, τ ⊆ U (resp. (R, U)σ, τ ⊆ U, and U is called a (σ, τ)-Jordan ideal if U is both a (σ, τ)-right Jordan ideal and a (σ, τ)-left Jordan ideal of R. A (σ, τ)-Jordan ideal U of R is said to be a (σ, τ)- ⋆-Jordan ideal if U ⋆ = U. In the present paper, it is shown that if U is commutative, then R is commutative. The commutativity of R is also obtained if (U , U)σ, τ ⊆ Cσ, τ(R). Some more results are obtained on the ⋆-prime ring with a characteristic different from 2. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with non-zero identity and I its proper ideal. The total graph of R with respect to I, denoted by T (ΓI (R)), is the undirected graph with all elements of R as vertices, and where distinct vertices x and y are adjacent if and only if x + y ∈ S (I) = { a ∈ R : r a ∈ I  for some  r ∈ R \ I }. In this paper, some bounds for the genus of T(ΓI(R)) are obtained. We improve and generalize some results for the total graphs of commutative rings. In addition, we obtain an isomorphism relation between two ideal based total graphs. [ABSTRACT FROM AUTHOR]

In this paper, we give a list of identities which are equivalent to modular law. The identities are divided into various small groups for the convenience in proofs. [ABSTRACT FROM AUTHOR]

In this paper, the question of the in-between situation is addressed through a clinical consideration of a patient with HIV, called Victor, who helps us think about the issue of sexual and generational indifferentiation. In conjunction with the construction of identity, the question of the in-between situation will be developed in its narcissistic dimension and its link with the Ideal, particularly through the notion of shame and guilt. This theoretical and clinical consideration is based on psychodrama sessions featuring hippocampus, violent men and finally a little wolf: a chaotic course, however therapeutic, starting with violent indifferentiation and leading to a soothing differentiation. [ABSTRACT FROM AUTHOR]

The goal of this paper is to introduce the concept of λ-statistical convergence of weight g of fuzzy numbers by using ideal. In addition to this concept, some inclusion theorems are also presented. [ABSTRACT FROM AUTHOR]

In this paper the concepts of pure fuzzy and weakly pure fuzzy ideals in ordered semigroups are introduced. Characterizations of right weakly regular ordered semigroups by fuzzy ideals are discussed. Also, we obtain that for each pure fuzzy ideal of ordered semigroups is weakly pure. [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]

In this paper we have introduced two new types of sets termed as I* -open sets and strongly I* -open sets and discussed some of its properties. The relation between similar types of sets, characterizations and some basic properties of such sets have been studied. [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]

In this paper we introduce upper/lower m-I-continuous multifunctions as a multifunction defined on an ideal minimal space (X; m; I). We obtain some characterizations and several properties of such multifunctions. As special cases of these properties, we obtain the properties of upper/lower -I-continuous [4], upper/lower semi-I- continuous [3] and upper/lower pre-I-continuous [3] multifunctions. [ABSTRACT FROM AUTHOR]

Basic algebras were introduced by Chajda, Halaš and Kühr as a common generalization of MV-algebras and orthomodular lattices, i.e. algebras used for formalization of non-classical logics, in particular the logic of quantum mechanics. These algebras were represented by means of lattices with section involutions. On the other hand, classical logic was formalized by means of Boolean algebras which can be converted into Boolean rings. A natural question arises if a similar representation exists also for basic algebras. Several attempts were already realized by the authors, see the references. Now we show that if a basic algebra is commutative then there exists a representation via certain semirings with involution similarly as it was done for MV-algebras by Belluce, Di Nola and Ferraioli. These so-called basic semirings, their ideals and congruences are studied in the paper. [ABSTRACT FROM AUTHOR]

New approaches in topology or related branches of mathematics have contributed in a valuable way to the science, and have yielded various new topics for investigation. The main goal of this paper is to examine a new approach and so a new form of open sets via elements of an ideal. The concept of α*I-open sets is introduced and discussed. [ABSTRACT FROM AUTHOR]

Abstract In this paper we primarily introduce certain new versions of groupability, namely star- I -groupability which is introduced using both star operation and the notion of ideals and then a more general notion of R -groupability. We establish several results regarding these groupability notions in the process of extending certain existing results on groupability. [ABSTRACT FROM AUTHOR]

In this paper, following a very recent and new approach of [1], we further generalize recently introduced summability methods in [6] (where ideals of N were used to extend certain important summability methods) and introduce new notions, namely, I-statistical convergence of weight g and I-lacunary statistical convergence of weight g, where g : N → [0;∞) is a function satisfying g (n) → ∞ and n/g (n) → 0. We mainly investigate their relationship and also make some observations about these classes. Our results extend the recent results of [7]. [ABSTRACT FROM AUTHOR]

Fuzzy sets, formalized by Zadeh in 1965, generalizes the classical idea of sets. The idea itself was generalized in 1975 when Zadeh introduced the interval-valued fuzzy sets. In this paper, we generalize further the above concepts by introducing interval-valued fuzzy on ideal sets, where an ideal is a nonempty collection of sets with a property describing the notion of smallness. We develop its basic concepts and properties and consider how one can create mappings of interval-valued fuzzy on ideal sets from mappings of ordinary sets. We then consider topology and continuity with respect to these sets. [ABSTRACT FROM AUTHOR]

In this paper, we introduce β-paracompactness with respect to an ideal (I-β-paracompactness) as a weak form of β-paracompactness and I-paracompactness. We give some relations between this concept and some other types of paracompactness, and also we study some of its fundamental properties. [ABSTRACT FROM AUTHOR]

This paper mainly dedicated on overview of zero sets in Ideal topological spaces. We also introduce a new class of functions which generalizes the class of continuous functions and investigate its position in the hierarchy of continuous functions on Ideal topological spaces. Moreover, these new sets (zero*-I-set) which is a pragmatic approach to characterize completely Hausdorff spaces. [ABSTRACT FROM AUTHOR]

In this paper, we make further investigation on I- convergence of filters and introduce I- closed sets in a topological space. We have used I- closed sets to determine topology on an arbitrary set. [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]

The notion of β1-paracompactness in topological spaces is introduced and studied in [1]. In this paper, we introduce and investigate the notion of β1-paracompact spaces with respect to an ideal I which is a generalization of the notion of β1-paracompact spaces. We study characterizations, subsets and subspaces of β1I-paracompact spaces. Also, we investigate the invariants of β1I-paracompact spaces by functions. [ABSTRACT FROM AUTHOR]

In this paper, the concepts of n-fold implicative ideals and n-fold obstinate ideals in BL-algebras are introduced. With respect to this concepts, some related results are given. In particular, it is proved that an ideal is an n-fold implicative ideal if and only if is an n-fold Boolean ideal. Also, it is shown that a BL-algebra is an n-fold integral BL-algebra if and only if trivial ideal {0} is an n-fold obstinate ideal. Moreover, the relation between n-fold obstinate ideals and n-fold (integral) obstinate filters in BL-algebras are studied by using the set of complement elements. Finally, it is proved that ideal I of BL-algebra L is an n-fold obstinate ideal if and only if L/I is an n-fold obstinate BL-algebra. [ABSTRACT FROM AUTHOR]

This paper provides an in‐depth analysis of how computer algebra systems and CSP solvers can be used to deal with the problem of enumerating and distributing the set of r×s partial Latin rectangles based on n symbols according to their weight, shape, type, or structure. The computation of Hilbert functions and triangular systems of radical ideals enables us to solve this problem for all r,s,n≤6. As a by‐product, explicit formulas are determined for the number of partial Latin rectangles of weight up to 6. Further, to illustrate the effectiveness of the computational method, we focus on the enumeration of 3 subsets: (1) noncompressible and regular, (2) totally symmetric, and (3) totally conjugate orthogonal partial Latin squares. In particular, the former enables us to enumerate the set of seminets of point rank up to 8 and to prove the existence of 2 new configurations of point rank 8. Finally, as an illustrative application, it is also exposed a method to construct totally symmetric partial Latin squares that gives rise, under certain conditions, to new families of Lie partial quasigroup rings. [ABSTRACT FROM AUTHOR]

In this paper, our aim is to introduce and study some new spaces of lacunary I - convergence for sequence of fuzzy real number which are defined by compact operator (T) on the real space ℝ. i.e., c F I θ (T) , c F 0 I θ (T) , ℓ F ∞ I θ (T) , ℓ F ∞ θ (T) and examine some basic properties and prove some inclusions relation on these spaces. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study triple difference sequence spaces over n-normed space via the sequence of modulus functions. Some algebraic and topological properties of the newly constructed spaces are also established. [ABSTRACT FROM AUTHOR]

We consider four classes of topological spaces which are defined with the aid of convergence with respect to ideals on N . All these classes are subclasses of countably compact spaces, and two of them are also subclasses of sequentially compact spaces. In the first part of the paper (Sections 1 and 2 ) we prove some properties of these classes. In the second part of the paper (Sections 3 and 4 ) we focus on spaces defined by two particular ideals connected with well known theorems in combinatorics, namely van der Waerden's theorem and Hindman's theorem. The main aim of this part of the paper is to show that two classes of the considered spaces coincide for the van der Waerden ideal and Hindman ideal respectively. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the description of hyperabelian Leibniz algebras, whose subideals are ideals. [ABSTRACT FROM AUTHOR]

Weighted uniform densities are a generalization of the uniform density, which is also known as the Banach density. In this paper, we introduce the concept of weighted uniform density ideals and consider the topological complexity of these ideals as well as when they have certain analytical properties related to the ideal convergence of sequences and series. Furthermore, we prove some inequalities between different upper and lower weighted uniform densities and give the answer to the problem concerning the Darboux property of these densities. [ABSTRACT FROM AUTHOR]

In this paper, we consider the well‐posedness issue for the density‐dependent incompressible viscoelastic fluids of the Oldroyd model for the ideal case in space dimension greater than 2. We obtain the local well‐posedness of this model under the assumption that the initial density is bounded away from zero in the critical Besov spaces by means of the Littlewood‐Paley theory and Bony's paradifferential calculus. In particular, we obtain a Beale‐Kato‐Majida–type regularity criterion. [ABSTRACT FROM AUTHOR]

Let R be a semiprime ring. A mapping F: R → R (not necessarily additive) is called a multiplicative (generalized) reverse derivation if there exists a map d: R → R (not necessarily a derivation nor an additive map) such that F(xy) = F(y)x + yd(x) for all x; y 2 R. In this paper we investigate some identities involving multiplicative (generalized) reverse derivation and prove some theorems in which we characterize these mappings. [ABSTRACT FROM AUTHOR]

In this paper, we study concepts of convergence and ideal convergence of sequence of functions and investigate relationships between them and some properties such as linearity in 2-normed spaces. Also, we prove a decomposition theorem for ideal convergent sequences of functions in 2-normed spaces. [ABSTRACT FROM AUTHOR]

In this paper we primarily consider the ideal analogue of Hurewicz property introduced recently by Das in [6] and subsequently introduce the ideal analogues of several versions of this very important property studied in the last decade. We establish certain inter relationships between the new notions presenting suitable examples as far as possible as well as prove many related results and in particular preservation properties. [ABSTRACT FROM AUTHOR]

In [3] Dündar introduced the notion of rough I2-convergence and obtained two criteria for rough I2-convergence. In the present paper we introduce some new rough ideal convergent sequence spaces of Musielak-Orlicz functions and four dimensional bounded- regular matrices. We study some topological and algebraic properties of these spaces. We also establish some inclusion relations between these spaces. Finally, we examine that these spaces are normal as well as monotone and sequence algebras. [ABSTRACT FROM AUTHOR]

In this paper, we identify the (0, *)-ideals of a demi-pseudocomplemented MS-algebra L as the kernel of the boolean congruences on L. In particular, we show that these ideals are precisely the kernels of the congruences # on L such that (L/v; *) is boolean, and that they form a sublattice of the lattice of ideals of L that is isomorphic to the interval [G, ι] of the congruence lattice of L where G is the Glivenko congruence and ι is the universal congruence. [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 paper discusses the topic of immortality in the pre-Islamic period and its role in constructing the character of an ideal man. Since the Arabs before Islam were softened by the issue of death, they dwelled on the topic of immortality though they knew it too well its impossibility. As they rejected mortality, they realized that the abstract immortality is the only way for them to be remembered after the mortality of the body that enticed the ideal man in the pre-historic period to do commendable deeds that other poets would mention them with or he would make it as a virtue in his poems; as ‘Antarah was known for his bravery, Hatim with his generosity and Samuel with his loyalty as they realized that their deeds will be remembered for the rest of the ages. The study highlighted on a number of the Pre-Islamic poems and concluded that those poets realized that their mortality was achievable in a subtle way but not physically. This seems to us- from the poems- the meaning of immortality, idealism and their realization of the meaning of mortality from what they witnessed from the natural scenes that take place around them; the means to immortalize themselves in a subtle way and the role of poems in achieving this aim. We also learned that they themselves were fully aware that immortality is possible only through the Arabic virtues that they so proudly adhered to. [ABSTRACT FROM AUTHOR]

The sequence space 𝐵BVσ was introduced and studied by Mursaleen [Houston J. Math. 9, 505-509 (1983; Zbl 0542.40003)]. The main aim of this paper is to study some new double sequence spaces of invariant means defined by ideal and modulus function. Furthermore, we also study several properties relevant to topological structures and inclusion relations between these spaces. [ABSTRACT FROM AUTHOR]

In order to accurately, robustly and efficiently simulate the three-dimensional (3D) interfacial flow problems with large density and viscosity ratio, we should, on the one hand, adopt the accurate and robust interface capturing method, on the other hand, use the efficient solution algorithm for coupling the velocity and pressure. In this paper, a coupled volume-of-fluid and level set (VOSET) method is applied to capture the two-phase interface, while an inner doubly iterative efficient algorithm for linked equations (IDEAL) is used to couple the velocity and pressure. Both of the VOSET method and the IDEAL algorithm were first proposed by the present author and further extended by other authors. Finally, the superiority of the VOSET method combined with the IDEAL algorithm (VOSET + IDEAL) is verified by three interfacial flow problems with large density and viscosity ratio. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of generalized terminal sections in BE-algebras and investigate their properties. Furthermore, these sets are considered in commutative and self distributive BE-algebras. Finally, we provide the relationship between self distributive and ideal and the relationship between self distributive and filter. [ABSTRACT FROM AUTHOR]