Several Properties of Green´s Relations on a Semiring

Green´s relations have played a fundamental role in the development of semi group theory. M.P. Grillet defined Green´s relations on a semiring in terms of principal ideals. In this paper, we mainly discuss the properties of left (right) Green´s relations on a semiring, the result show that La is the same as (a] whenever (a] is the minimal left ideal, and we give a sufficient and necessary condition for L = L.