Department of Mathematics, Jadavpur University Kolkata-700032, India manasi−[email protected] Abstract The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the notion of fuzzy set. In this paper we apply this concept of Atanassov to ideals, prime ideals and semiprime ideals of Γsemigroups in order to obtain some characterization theorems. We also introduce the not...

*Correspondence: [email protected] School of Mathematics Science, Liaocheng University, Liaocheng, Shandong 252059, China Abstract In order to generalize the notions of a (∈,∈ ∨q)-fuzzy subring and various (∈,∈ ∨q)-fuzzy ideals of a ring, a (λ,μ)-fuzzy subring and a (λ,μ)-fuzzy ideal of a ring are defined. The concepts of (λ,μ)-fuzzy semiprime, prime, semiprimary and primary ideals are introdu...

The separating space of a derivation onA is a separating ideal [2, Chapter 5]; it also satisfies the same property for the left products. The following assertions are of the most famous conjectures about derivations on Banach algebras: (C1) every derivation on a Banach algebra has a nilpotent separating ideal; (C2) every derivation on a semiprime Banach algebra is continuous; (C3) every derivat...

A left almost semigroup (LA-semigroup) or an Abel-Grassmann’s groupoid (AG-groupoid) is investigated in several papers. In this paper we have discussed ideals in LA-semigroups. Specifically, we have shown that every ideal in an LA-semigroup S with left identity e is prime if and only if it is idempotent and the set of ideals of S is totally ordered under inclusion. We have shown that an ideal o...

Abstract The aim of this paper is to investigate the behaviour prime and semiprime subgroups groups, their relation with existence abelian normal subgroups. In particular, we study set Spec( G ) all a group endowed Zariski topology and, among other examples, construct an infinite whose proper are form descending chain type ? + 1.

The aim of this paper is the study of fuzzy Γ-hyperrings. In this regard the notion of ν-fuzzy hyperideals of Γ-hyperrings are introduced and basic properties of them are investigated. In particular, the representation theorem for ν-fuzzy hyperideals are given and it is shown that the image of a ν-fuzzy hyperideal of a Γ-hyperring under a certain conditions is two-valued. Finally, the product o...