完全0-单半群的同态像和某些同余  

The Homomorphic Images of a Completely 0-simple Semigroup and Some Congruences on It

作　　者：张润石[1] 李艳[1] 喻秉钧[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2007年第2期146-150,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10471112)资助项目

摘　　要：证明了完全0-单半群的真同态像仍完全0-单,给出了其结构;刻画了完全0-单半群的最大真同余及其商;给出了有0和本原幂等元的半群S无同余的充要条件;讨论了完全0-单半群上的幂等元纯同余,幂等元分离同余及其同态像;给出了完全0-单半群存在0-群同余的充要条件并刻画了其0-群同态像.In this paper, it is proved that proper homomorphic images of a completely 0-simple semigroup are also completely 0- simple. The structure of the images is described. The maximum proper congruence on a completely 0-simple semigroup and its image are characterized. The sufficient and necessary condition for a semigroup with 0 and primitive idempotent to be congruence-free is given. Idempotet-pure and idempotent-separating congruences on a completely 0-simple semigroup and their images are discussed. The sufficient and necessary condition for a completely 0-simple semigroup to have 0-group congruence is given and the 0-group homomorphic images are characterized.

关 键 词：完全0-单半群 真同余 无同余 0-限制矩形带 幂等元纯同余 幂等元分离同余 0-群同余 

分 类 号：O152.7[理学—数学]