Some commutativity conditions for Gamma-Generalized Boolean Semiring

Utsanee Leerawat, Katthaleeya Daowsud

Abstract

In this paper, we investigate some properties of commutative Gamma-idealsin Gamma-generalized Boolean semiring. Also, we obtain commutativity of Gamma-generalizedBoolean semiring satisfying some suitable conditions. Furthermore, we investigatethe commutativity of prime Gamma-generalized Boolean semiring R possessing a non-identity commuting automorphism and satisfying right distribution: (b + c) alplha a =b alpha a + c alpha a for all a, b, c in R and alpha in Gamma.