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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 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]

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]

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]

In this paper we investigate the concept of ℐ {\mathcal{I}} -monotonic convergence of sequences of bi-complex numbers. We also discuss some partial order relations ≼ i 2 {\preccurlyeq_{i_{2}}} and ≼ i id {\preccurlyeq_{i_{\rm id}}} between two bi-complex numbers and ℐ {\mathcal{I}} -convergence, ℐ {\mathcal{I}} -monotonic sequences with respect to different partial order relations, ℐ {\mathcal{I}} -Cauchy sequences, ℐ {\mathcal{I}} -bounded monotonic sequences of bi-complex numbers. The analysis indicates that ℐ {\mathcal{I}} -monotonicity with respect to ≼ i 2 {\preccurlyeq_{i_{2}}} is not comparable with ℐ {\mathcal{I}} -monotonicity with respect to ≼ i id {\preccurlyeq_{i_{\rm id}}} . [ABSTRACT FROM AUTHOR]

Ideals and filters are important notions with different meanings in the study of algebraic structures related to logical systems. In this paper we establish new connections between these concepts in residuated lattices. [ABSTRACT FROM AUTHOR]

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]

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 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]

In this paper, we illustrate the rule for finding number of idempotents in the doubly stochastic matrix semigroup Dn and also locate the idempotents in the case of D3 and D4. Further, we describe idempotent generated ideals of these semigroups and it is shown that the idempotent generated ideals form a lattice. [ABSTRACT FROM AUTHOR]

In this paper, the concept of Paradistributive Latticoid (PDL) as a generalization of a distributive lattice is introduced and investigated its properties. A set of equivalent conditions for a PDL to become a distributive lattice are given. The notions of an ideal and a filter in a PDL are introduced and studied their properties. Subdirect representation of a PDL is obtained [ABSTRACT FROM AUTHOR]

In this paper, convergences of a filter and a net have been characterized through ideal on topological spaces. Furthermore, we characterized the local function in an ideal topological space in terms of convergence of filter. Using Zorn's Lemma, we have found a maximal element in the collection of all proper ideals on a nonempty set which is called maximal ideal. We provide a convenient characterization of maximal ideals. We also consider simple properties of the image of an ideal, a net and various local functions under a homeomorphism. [ABSTRACT FROM AUTHOR]

Let 풪풫ℰn be the monoid of all orientation-preserving and extensive full transformations on {1,…,n}. In this paper, first we discuss left and right abundance of the principal ideals of 풪풫ℰn. Second, we give necessary and sufficient conditions for the principal ideals of 풪풫ℰn to be abundant and regular. Finally, we study abundance of the ideals in 풪풫ℰn. [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 new notions of dimensions for ideal topological spaces are inserted, called *-quasi covering dimension and ideal quasi covering dimension. We study several of their properties and investigate their relations with types of covering dimensions like the-covering dimension and the ideal covering dimension. [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]