Studies On Several Types Of Semi-rings

Congruence relation plays an important role in algebraic theory of semiring. The goal of this dissertation is to study congruence openings which are related to Green’s relation on several different types of semirings.1. We study that congruence openings of a semiring that is determined by Green’s relations L,R of an ai-semiring and varieties which are related to congruence openings.2. We study that congruence openings of a semiring that is determined by Green’s relations of a semiring whose multiplicative semigroup satisfies xn+1≈x and three semiring varieties which are related to congruence openings. We investigate that the lattice of all subvarieties of the variety [xn+1≈x]∩OBG of semirings whose multiplicative semigroups are orthocryptogroups and satisfy xn+1≈x and obtain two closure operators on this lattice. Moreover, it is studied that some subvarieties of the semiring variety [xn+1≈x]∩OBG.3. We study the varieties generated by ai-semirings of order two. It is studied that some subvarieties of the variety S2generated by all ai-semirings of order two. We define some congruences which are related to elements of a semiring in S2and show the relationships of these congruences.