Four Constructions Of Semirings Of Additive Idempotent Elements

Additively idempotent semiring is one of the most important subjects in semiring algebraic theory.In this thesis we study four types of constructions of additively idempotent semirings.The main results are as follows:Let S be an additivly idempotent semiring.1.We study the additively idempotent semiring S0.We show that the variety generated by S0 contains the distributive lattice of order two.We reveal the relation between the identities of S0 and the identities of S.We establish a necessary and sufficient condition such that S0 is finitely based.2.We study the additively idempotent semiring S(0).We show that the variety generated by S0 is the join of the variety generated by S and the variety generated by the monogenic bisemilattice of order two.3.We study the additively idempotent semiring S1.We show that the variety generated by S1 contains the distributive lattice of order two.4.We study the additively idempotent semiring S(1).We show that the variety generated by S1 contains the monogenic bisemilattice of order two.