FUZZY RADICALS OF Γ-SEMIRINGS

Sarbani Goswami; Sujit Kumar Sardar

Sarbani Goswami
Sujit Kumar Sardar

Keywords: Fuzzy prime radical, Fuzzy nil radical, Fuzzy primary ideal,Fuzzy prime ideal, Fuzzy semiprime ideal, Γ−semiring, left (right) operator semiring

Abstract

In this paper we introduce the notions of fuzzy prime radical and fuzzy nil radical of a fuzzy ideal in Γ−semiring and obtain some characterizations of these radicals. We also introduce the notion of Fuzzy primary ideal of a Γ−semiring and study it using fuzzy prime radical. Among other results we prove that in a commutative Γ−semiring, the concepts of fuzzy prime radical and fuzzy nil radical of a fuzzy ideal coincide.