This paper is devoted to the foldness theory of implicative ideals in BCK-algebras. We use the fuzzy point concept to give some characterizations of fuzzy n-fold implicative ideals and establish some relationships with various n-fold ideals. We also construct some algorithms for studying the foldness of implicative ideals in BCK-algebras. AMS Mathematics Subject Classification: 06F35, 13A15, 8A...

Let I be any index set. We consider the Banach algebra Ce + l(I) with the Hadamard product, and prove that its Bass and topological stable ranks are both equal to 1. We also characterize divisors, maximal ideals, closed ideals and closed principal ideals. For I = N we also characterize all prime z-ideals in this Banach algebra.

In this paper, a new approach to LA-semigroup theory is proposed by obtaining significant characterizations of regular, intra-regular, completely regular, weakly regular and quasi-regular LA-semigroups via soft intersection left (right, two-sided) ideals, (generalized) bi-ideals, interior ideals, quasi-ideals of LA-semigroups.

We introduce the notion of bipolar fuzzy Lie sub-superalgebras (resp. bipolar fuzzy ideals) and present some of their properties. First we investigate the properties of bipolar fuzzy Lie sub-superalgebras and bipolar fuzzy ideals under homomorphisms of Lie superalgebras. Next we study bipolar fuzzy bracket product, solvable bipolar fuzzy ideals and nilpotent bipolar fuzzy ideals of Lie superalg...

In this paper, we define a new algebraic structure of an induced fuzzy k-ideal of a HX ring and some related properties are investigated. The purpose of this study is to implement the fuzzy set theory and ring theory in fuzzy HX k-ideals of a HX ring. We also establish the relation between fuzzy HX ideals and fuzzy HX k-ideals of a HX ring . Characterizations of level subsets of a fuzzy HX k-id...

Let S be an ordered semigroup. In this paper we first introduce the concepts of (∈,∈ ∨q)-fuzzy ideals, (∈,∈ ∨q)-fuzzy bi-ideals and (∈,∈ ∨q)-fuzzy generalized bi-ideals of an ordered semigroup S, and investigate their related properties. Furthermore, we also define the upper and lower parts of fuzzy subsets of an ordered semigroup S, and investigate the properties of (∈,∈ ∨q)-fuzzy ideals of S....

There exists an analogy between the structure of ideals of a cone in a right-ordered group and the structure of ideals of a Dubrovin valuation ring in a simple artinian ring. The structure of ideals of rank one cones and rank one Dubrovin valuation rings can be described completely. One sided versions of this problem are considered in 5] where the ideal theory of right cones is developed and a ...

In many applied disciplines like computer science, coding theory and formal languages, the use of fuzzified algebraic structures play a remarkable role. In this paper, we introduced some new types of generalization of an intuitionistic fuzzy interior ideal, called (α, β)-intuitionistic interior ideals of an ordered semigroup S. The important milestone of this paper is to link the ordinary inter...

We provide some new conditions under which the graded Betti numbers of a mono-mial ideal can be computed in terms of the graded Betti numbers of smaller ideals, thus complementing Eliahou and Kervaire's splitting approach. As applications, we show that edge ideals of graphs are splittable, and we provide an iterative method for computing the Betti numbers of the cover ideals of Cohen-Macaulay b...

The notions of intuitionistic fuzzy T-ideals in BCI-algebras are introduced.Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy T-idealare provided. Using a collection of T-ideals, intuitionistic fuzzy T-ideals areestablished.