let $r$ be a commutative ring with identity‎. ‎a proper ideal $p$ of $r$ is a $(n-1,n)$-$phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin r$‎, ‎$a_1cdots a_nin pbackslash p^m$ ($a_1cdots a_nin pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin p$‎, ‎for some $iin{1,ldots,n}$; ($m,ngeq 2$)‎. ‎in this paper several results concerning $(n-1,n)$-$phi_m$-prime and $(n-1,n)$-...

The purpose of this paper is to study soft sets and soft topological spaces. We also introduce the concepts of soft interior point, soft interior, soft neighborhood, soft continuity and soft compactness. The relationships between soft topology and fuzzy topology are also provided. Also, some basic properties of these concepts are explored. 2010 AMS Classification: 06D72, 54A40

The purpose of this paper is the study of algebraic properties of soft sets in BCC-algebras. In this regards we introduce and study soft ideals and idealistic soft BCC-algebras.

This paper is part of an eight paper project [14]-[20] studying the arithmetic mean operator ideals in B(H) introduced by Dykema, Figiel, Weiss and Wodzicki in [10]. Every ideal I is generated by diagonal operators with positive decreasing sequences, and its arithmetic mean ideal Ia is generated by diagonal operators with the arithmetic means of those sequences. In this paper we focus on lattic...

The first step towards near-rings was an axiomatic research done by Dickson in 1905. In 1936, it was Zassenhaus who used the name near-ring. Many parts of the well established theory of rings are transferred to near-rings and new specific features of near-rings have been discovered. To deal with the idea of near-rings using ternary product Warud Nakkhasen and Bundit Pibaljommee have applied the...

In this paper, we introduce the notions of (∈,∈ ∨ q)-N -ideals and (γ, δ)-N -ideals of subtraction algebras, which are generalization of N -ideals. Some characterization for these generalized N -ideals are derived. Also, we introduce the notions of (∈,∈ ∨ q)-N -ideals and N -ideals with thresholds of subtraction algebras. The characterization of N -ideals with thresholds by their closed (f, t)-...

Notions of core, support, and inversion of a soft set have been defined and studied. Soft approximations are soft sets developed through core and support and are used for granulating the soft space. Membership structure of a soft set has been probed in and many interesting properties are presented. We present a new conjecture to solve an optimum choice problem. Our Example 31 presents a case wh...

In this paper the concept of fuzzy characteristic interior ideals in partially ordered Γ-semigroups(Po-Γ-semigroups) has been introduced. It is observed that it satisfies level subset criterion and characteristic function criterion. Mathematics Subject Classification: 08A72, 3F55, 20M12

Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft normed rings by soft set theory. The notions of soft normed rings, soft normed ideals, soft complete normed rings are introduced and also several related properties and examples are given.

In this paper, the notation of interior KU-algebra and some related definitions are introduced. Various characterisations for have been proved. The concept positive implicative prove results regarding also presented. addition, KU-ideals several properties these ideals