Semigroup. Additive Completely Regular Semigroups Half Bad

The study of the theory of semirings is one of the important topics in algebra. We mainly study the structures of semiring with a completely regular additive semigroup from the angle of semigroups in this paper.The dissertation consists of fivee chapters.The first chapter includes the basic notations and definition.We introduce some concepts and theories related to Semirrings,and recall the notations ang results of Completely Regular Semiring which will be used in the following.In chapter two,we characterize te properties of subdirect products of Semiring Which Multiplicative Reducts are Completely Regular Semigroups.In chapter three,We studies the characterazations of Semiring Which Multiplicative Reducts are Regular Orthocryptogroups,and we investigate the relationships between the classea of Semiring Which Multiplicative Reducts are Orthocryptogroups In chapter four,We give the equivalent characterizations of which the Green relations(?) and(?) are congruences on S.In chapter five,WE characterize the properties of Semirings belonging to(?), and proved that(?) is a semiring congruence.