Congruences on an Orthodox Semigroup  

作　　者：李勇华 

机构地区：[1]Department of Mathematics, South China Normal University, Guangzhou, 510631

出　　处：《Northeastern Mathematical Journal》2004年第3期291-302,共12页东北数学(英文版)

基　　金：The NNSF (19970128) of China and the NSF ((011438), (021073), (Z02017)) of Guangdong Province.

摘　　要：Let 5 be an orthodox semigroup and γ the least inverse congruence on 5. C(S) denotes the set of all congruences on S. In this paper we introduce the concept of admissible triples for S, where admissible triples are constructed by the congruences on S/γ , the equivalences on E(S)/L and E(S)/R. The notation Ca(S) denotes the set of all admissible triple for S. We prove that every congruence ρ on S can be uniquely determined by the admissible triple induced by ρ, and there exists a lattice isomomorphism between C(S) and Ca(S).Let 5 be an orthodox semigroup and γ the least inverse congruence on 5. C(S) denotes the set of all congruences on S. In this paper we introduce the concept of admissible triples for S, where admissible triples are constructed by the congruences on S/γ , the equivalences on E(S)/L and E(S)/R. The notation Ca(S) denotes the set of all admissible triple for S. We prove that every congruence ρ on S can be uniquely determined by the admissible triple induced by ρ, and there exists a lattice isomomorphism between C(S) and Ca(S).

关 键 词：Orthodox semigroup CONGRUENCE admissible triple normal equivalence 

分 类 号：O152.7[理学—数学]