Semigroup On The Pseudo-similar And Semi-similar To The Relationship,

The research of semigroup plays an important role in the research of the theory of algebra, and the Green's equivalences are especially significant in the study of semigroups.In this dissertation, we mainly disscuss Pseudo-similarity and Semisimilarity of the semigroups which satisfy the identity x~n≈ x, and then discuss the relations among Pseudo-similarity, Semisimilarity and Green's D relation. We have three chapters. In chapter one, we introduce related knowledge of the completely semigroup theory. In chapter two, we first get characterization of Pseudo-similarity for semigroups which satisfy the identity x~n≈ x. And then, we mainly discuss the relations among Pseudo-similarity, Semisimilarity and Green's D(L, R.) relation on this semigroups satisfying above-mentioned identity. In chapter three, we mainly discuss one kind of special binary relation, and get some properties of this relation which on the union of two cyclic groups.