Several Classes Of Unipotent Semiring

Algebraic theory of idempotent semirings is one of the active fields of algebra. The goal of this dissertation is to study some properties and structure of idempotents semirings with identity and how to add an identity element to semirings.It mainly achieved in the following aspects:1.Some properties of the members of four varieties of idempotent semirings with identity.Some properties of the members with identity of four varieties (?)oD,(?)oM,(?)oD and(?)oM are given.2.Some equivalent characterizations and structure of the members of four varieties of idempotent semirings with identify.Some equivalent characterizations of the members of those four varieties((?)oD)₁,((?)oM)₁,((?)oD)₁ and((?)oM)₁ are given by using the following four conditions:identities of varieties,partial orders on idempotent semirings,Green's relations on semiring and four subvarieties with simple form introduced in chapter two.Next we studied the structure of the members of these four varieties and relations between the members and monobisemilattice,distributive lattice.3.We studied how to add an identity element to semirings and some properties of semirings with identity.We know how to add an zero element to semirings. Also we studied how to add an identity element to semirings with some conditions.Some properties of these new semirings with identity are obtained.