Varieties Generated By Some Semirings Of Order Two

The finite basis problem for varieties is one of the important subjects in algebra.Up to isomorphism,there are exactly 10 semirings of order 2.In this thesis we mainly study the varieties generated by some semirings of order two.The mainly results are as follows:Firstly,we study the variety Ag generated by M2,D2,N2,T2,Z1,Z2 Z7 and Z8.We prove that this variety is finitely based and provide the equational basis for it.Secondly,we study the variety S9 generated by L2,R2,M2,D2,N2,T2,Z1,Z2 and Z7.We prove that this variety is finitely based.Moreover,we give the equational basis for it.