Prime Fuzzy Ideals of a Gamma Semiring -1

Abstract

Objectives:The main objective of this article is to introduce some fundamental results of fuzzy ideals and Prime fuzzy ideals of a Γ− semiring R . Methods: We use some fundamental results of fuzzy ideals and conditions like semi subtractive, centreless etc. for developments of the main results. Findings: In this connection, we establish some important results of fuzzy ideals and prime fuzzy ideals of semirings to Γ− semirings. Novelty: We find a special class of fuzzy ideals of a Γ− semiring R and with this, construct a lattice ordered Γ− semiring. Further, we find that a fuzzy ideal of Γ− semiring R can be a decreasing map from [0, 1] into the set of R together with an empty set. As an application of this result, the prime fuzzy ideals of a Γ− semiring R are described in terms of prime ideals of a Γ− semiring R.