Some Partial Orders And L-related Congruence On Completely Regular Semigroups

In this thesis, we mainly investigate some partial orders M,B,P on completely regular semigroups and (?)-related congruence. We characterize three special cryp-togroups by three partial orders.Finaly. we give definition of (?)-related cogruence and an equivalent characterization.This thesis consists of three chapters.In the first chapter, some basis concepts and lemmas are proposed.In the second chapter, we give three binary relations M, B, P, and give suffi-cient and necessary condition which M.P arc partial orders on S. Moreover, we prove that a completely regular semigroup S is a left cryptogroup if and only if M-≤, S is a local regular cryptogroup if and only if B=≤and S is a local left regular cryptogroup if and only if P-≤.In the third chapter, we mainly give an equivalent characterization of (?)-related congruence.