notions of strongly regular, regular and left(right) regular $gamma$−semigroupsare introduced. equivalent conditions are obtained through fuzzy notion for a$gamma$−semigroup to be either strongly regular or regular or left regular.

The purpose of this paper is to introduce and discuss the concept of T-rough (prime, primary) ideal and T-rough fuzzy (prime, primary) ideal in a commutative ring . Our main aim in this paper is, generalization of theorems which have been proved in [6, 7, 11]. At first, T-rough sets introduced by Davvaz in [6]. By using the paper, we define a concept of T-rough ideal , T-rough quotient ideal an...

The notions of prime(semiprime) fuzzy h-ideal(h-biideal, h-quasi-ideal) in Γ-hemiring are introduced and some of their characterizations are obtained by using ”belongingness(∈)” and ”quasi − coincidence(q)”. Cartesian product of prime(semiprime) fuzzy h-ideals of Γ-hemirings are also investigated. Keywords—Γ-hemiring, Fuzzy h-ideals, Prime fuzzy left h-ideal, Prime(semiprime) (∈,∈ ∨q)-fuzzy lef...

We introduce the notion of reset left regular decomposition of an ideal regular language and we prove that there is a one-to-one correspondence between these decompositions and strongly connected synchronizing automata. We show that each ideal regular language has at least a reset left regular decomposition. As a consequence each ideal regular language is the set of synchronizing words of some ...

We prove that if the initial ideal of a prime ideal is Borel-fixed and the dimension of the quotient ring is less than or equal to two, then given any non-minimal associated prime ideal of the initial ideal it contains another associated prime ideal of dimension one larger. Let R = k[x1, x2, . . . , xr] be a polynomial ring over a field. We will say that an ideal I ⊆ R has the saturated chain p...

In this paper we introduce the concept of ideal elements in poe-AG-groupoid and give some characterizations and properties of their ideal elements. So we consider some results concerning ideals in poe-semigroups and investigate them in poe-AG-groupoids. Also, the class of ideal elements of poe-AG-groupoids are studied, certain intrinsic and basic properties of poe-AG-groupoids including: ideal,...

In this paper, with a new idea, we redefine generalized fuzzy ideal and investigate some of its properties. We generalize fuzzy prime ideals and introduce the notions of (∈,∈ ∨q)−fuzzy prime ideal of ordered semigroups. We characterize (∈,∈ ∨q)−fuzzy prime ideal by its image and level ideals. We establish necessary and sufficient condition for fuzzy set to be a (∈,∈ ∨q)−fuzzy prime ideal. 2010 ...