The Properties Of Some Completely Regular Semirings

In this dissertation,we devote to study some special semirings,in which the additive reducts of semirings are semilattices and the multiplicative reducts are rectangular group and normal orthocryptogroup,respectively,we obtain some properties of semirings in these classes.There are three chapters in this paper.In chapter one,there are preface and introduction. In chapter two,we consider semirings whose additive reducts are semilattice and multiplicative reducts are rectangular group and their partial orders and prove its Green-(?), (?),(?) relations are semiring congruence,finally,give equivalent describe of(?) is semiring congruence.In chapter three,we investigate semirings whose additive reducts are semilattice and nmltiplicative reducts are normal orthocryptogroup,prove its Green(?),(?),(?) relations are semiring congruence and obtain some properties of these semirings.