Hopf理想模条件  

Hopf ideal Module Condition

作　　者：陈家鼐[1] 胡全[1] 

机构地区：[1]首都师范大学数学系

出　　处：《首都师范大学学报（自然科学版）》1996年第1期8-13,共6页Journal of Capital Normal University：Natural Science Edition

基　　金：国家自然科学基金

摘　　要：设Ｈ是有限维Ｈｏｐｆ代数，Ａ－是右Ｈ余模代数．记Ａ的Ｈ－不变子代数ＡＨ为Ｂ．在第１部分中，本文引进了Ａ是Ｂ－理想模的概念．定理１和２证明了Ａ是Ｂ－理想模当且仅当Ａ作为Ａ＃Ｈ－模是自生成子且是内投射的．定理３证明了若Ａ是Ｂ－理想模，则环Ｂ上的链条件可以传递到左Ａ＃Ｈ－模Ａ上．在．第２部分中，本文讨论了理想模条件与Ａ＃Ｈ和Ｂ之间的Ｍｏｒｉｔａ等价之间的联系．定理２和３证明了，当Ａ／Ｂ是右Ｈ－Ｇａｌｏｉｓ扩张或迹函数ｔ：Ａ→Ｂ是满射且Ａ是右Ｎｏｅｔｈｅｒ环时。Let H be a finite-dimensional Hop f algebra and A a right H-comodule algebra. Denote B=AH, the H-invariant subalgebra of A. In the first part of the paper, we introduce the notion of B-ideal module for A. We show in theorem 1 and 2 that A is a B-ideal module if and only if A as an A #H-module is a self-generator and intrinsically projective. In theorem 3 we show that the chain conditions on the ring B can be transferred to the left A# H module A. In the second part we discuss the interrelation between the condition of A being a B-ideal module and the Morita equivalence between A #H and B. Theorem 2 and 3 show that if A/B is a right H-extension or the trace function t:A→B is surjective with A being right noetherian, than A is a B-ideal module if and only if A# H' and B are Morita equivalent.

关 键 词：理想模条件 MORITA等价 内投射模 郝普夫代数 

分 类 号：O153.3[理学—数学]