Nil-extensions of completely simple semirings

Abstract

A semiring S is said to be a quasi completely regular semiring if for any a2 S there exists a positive integern such thatna is completely regular. The present paper is devoted to the study of completely Archimedean semirings. We show that a semiring S is a completely Archimedean semiring if and only if it is a nil-extension of a completely simple semiring. This result extends the crucial structure theorem of completely Archimedean semigroup.