Cleft扩张下的余纯投射维数

吉林大学学报(理学版)

Cleft扩张下的余纯投射维数

陈秀丽, 陈建龙

东南大学数学系, 南京 210096

收稿日期:2014-11-21 出版日期:2015-03-26 发布日期:2015-03-24
通讯作者: 陈建龙 E-mail:jlchen@seu.edu.cn

Copure Projective Dimensions under Cleft Extension

CHEN Xiuli, CHEN Jianlong

Department of Mathematics, Southeast University, Nanjing 210096, China

Received:2014-11-21 Online:2015-03-26 Published:2015-03-24
Contact: CHEN Jianlong E-mail:jlchen@seu.edu.cn

摘要/Abstract

摘要：

令H为有限维Hopf代数且A为固定域k上的代数, AB为H-cleft扩张. 利用cleft扩张和交叉积间的关系, 证明了当H半单时, 在cleft扩张下左余纯投射维数是不变的, 并给出了\%A与B\%的QF性质.

关键词: cleft扩张, 余纯投射维数, QF环

Abstract:

Let H be a finite dimensional Hopf algebra and A be an algebra over a fixed field k, using the relations between cleft extension and crossed product, we proved that the left copure projective dimension is invariant under cleft extensions when H is semisimple. At the same time, QF properties about A and B was investigated based on the assumption that AB is Hcleft.

Key words: cleft extension, copure projective dimension, QF ring

中图分类号:

O153.3

陈秀丽, 陈建龙. Cleft扩张下的余纯投射维数[J]. 吉林大学学报(理学版), 2015, 53(02): 264-266.

CHEN Xiuli, CHEN Jianlong. Copure Projective Dimensions under Cleft Extension[J]. Journal of Jilin University Science Edition, 2015, 53(02): 264-266.

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