Strongly Clean Semiring

Abstract

In this paper, we study the concept of strongly clean semiring. Let S be a semiring. An element \(a\in S\) is called strongly clean if \(a = e + u\) with e an idempotent in S and u a unit in S such that \(eu=ue\). A semiring S is said to be strongly clean if every nonzero element of S is strongly clean. We mainly study the notion of strongly clean semiring and obtain some important characterizations of strongly clean semiring in connection with exchange semiring, antisimple semiring and inverse semiring.