偏序群S上S-偏序系的内射包  

Injective Hulls of S-Posets Over a Pogroup S

作　　者：张霞[1,2] 徐彦涛 

机构地区：[1]华南师范大学数学科学学院,广州510631 [2]Department of Mathematics,Southern Illinois University Carbondale

出　　处：《华南师范大学学报（自然科学版）》2014年第4期12-15,共4页Journal of South China Normal University(Natural Science Edition)

基　　金：教育部高等学校博士学科专项科研基金项目(20124407120004)

摘　　要：偏序幺半群S上的S-偏序系是S-系理论的推广.设S是一个偏序群,应用S-系理论及序理论的方法,讨论了S-偏序系范畴的内射元,得出每个S-偏序系AS都存在唯一的内射包,并具体构造了AS的内射包.在此基础上,进一步得出AS的内射包既是A的极小内射扩张,又是A的极大本质扩张.An S - poset is a generalization of an S - act for a pomonoid S. Let S be a pogroup. In this work, by using S - act theory and partially order theory, injectives in the category of S - posets are studied. It is obtained that for any S - poset As, As admits an injective hull, which is unique up to isomorphism. Furthermore, the injective hull of As is necessarily a minimal injective extension and a maximal essential extension of A, and vice versa.

关 键 词：偏序群 S-偏序系 内射 内射包 

分 类 号：O152.6[理学—数学]