On S-acts containing no maximal S-subacts  

不包含极大子系的S-系(英文)

作　　者：石小平[1] 

机构地区：[1]东南大学理学院,南京210096

出　　处：《Journal of Southeast University(English Edition)》2006年第4期593-596,共4页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China(No10626012), Jiangsu Planned Projects for Postdoctoral ResearchFund(No0502022B)

摘　　要：Let S be a semigroup and let A be an S-act. Some necessary and sufficient conditions that S-subacts of A are maximal S-subacts are given. A relation B which is similar to the Green relation in semigroups is defined. By the relation B, it is proved that a non-empty set L of A is a maximal S-subact if and only if A／L is a （maximal） B-class. Finally, the concept of a C-subact is defined, some properties of C-subacts are discussed, and it is proved that A contains no maximal S-subacts if and only if every cyclic S-subact of A is a C-subact. Consequently, the results obtained by Imrich Fabrici that semigroups contain no maximal （left） ideals are the corollary of this paper.设S是半群,A是S-系.首先给出了A的子系是极大子系的充分必要条件;其次利用所定义的L关系,证明了A的非空子集L是A的极大子系的充分必要条件是A\L是A的(极大)L-类;最后,定义了C-子系的概念,讨论了其性质,并利用C-子系刻画了一类S-系.证明了S-系不包含极大子系当且仅当每一个循环子系是C-子系.从而Imrich Fabrici关于半群不包含极大(左)理想的主要结论就是本文的推论.

关 键 词：S-ACT maximal subact C-subact 

分 类 号：O152.7[理学—数学]