• ON THE ADDITIVE AND MULTIPLICATIVE STRUCTURE OF SEMIRINGS

Abstract

Let (S, +, •) be a semiring and (S, +, •, ) be a totally ordered semiring (t.o.s.r.). In this paper, we study the structure of semirings which are positive rational domains. It is established that in a PRD semiring (S, +, •), the set of additive idempotents is a completely prime multiplicative Ideal and (S,+) is a commutative semigroup if (S,+) is cancellative. We also study the structure of totally ordered semirings.