Some Studies On Two Classes Of Semirins

In this thesis,we mainly give the characterizations and structures of twoclasses of semirings. Particularly, we investigate the congruences on an or-thodox semiring whose additive idempotents satisfy permutation identities.We divide the thesis into three chapters.In Chapter1, we introduce several stages of the development of semiringtheory and its important position in mathematics, and give some relatedknowledge about the following chapters.In Chapter2, the investigation of congruences on generalized inversesemigroups is initiated. Following some properties of such semigroups, thecongruences on an orthodox semiring whose idempotents satisfy permuta-tion identities are established. In addition, we give a structure theorem ofhomomorphic image of this kind of orthodox semirings.In Chapter3, we discuss a special kind of orthodox semirings, and givesome characterizations of these semirings.