Study On Two Types Of Completely Regular Semiring

The study of the theory of semirings is one of the important topics in alge-bra.In this paper,we mainly study two classes of semirings for which the additive reduct is regular orthocryptogroup and the multiplicative reduct is regular or-thocryptogroup.There are three chapters.In chapter one,the background and the present sit-uation about semigroups and semirings are introduced.What's more, basic defi-nitions and notations which will be used in the following are also introduced.In chapter two,the class of semirings for which the additive reduct is regular or-thocryptogroup are studied. And its decomposition of subdirect products from different angles is given. Moreover,the subclass of these semirings are char-acterized. Meanwhile, the relation between the subclass of these semirings is also investigated.In chapter three,the class of semirings for which the multiplica-tive reduct is regular orthocryptogroup are studied.The definition about refined frame of semirings is also given.Further,the necessary and sufficient condition about the class of semirings is got.