半准素环的X-Gorenstein整体投射维数

吉林大学学报(理学版) ›› 2018, Vol. 56 ›› Issue (5): 1136-1139.

半准素环的X-Gorenstein整体投射维数

赵志兵

安徽大学数学科学学院, 合肥 230601

收稿日期:2018-05-02 出版日期:2018-09-26 发布日期:2018-11-22
通讯作者: 赵志兵 E-mail:zbzhao@ahu.edu.cn

Gorenstein Global Projective Dimension of Semiprimary Rings

ZHAO Zhibing

School of Mathematical Sciences, Anhui University, Hefei 230601, China

Received:2018-05-02 Online:2018-09-26 Published:2018-11-22

摘要/Abstract

摘要： 利用同调代数和相对同调代数中处理同调维数的方法, 证明半准素环的（左）X-Gorenstein整体投射维数等于其上所有单模的（左）X-Gorenstein投射维数的上确界, 并给出一些相关应用.

关键词: 半准素环, Gorenstein投射模, X-Gorenstein投射模, X-Gorenstein(整体)投射维数

Abstract: By using the method for handling homological dimension in homological algebra and relative homological algebra, the author proved that the (left) X-Gorenstein global projective dimension of a semiprimary ring was equal to the supremum of the set of (left) X-Gorenstein projective dimensions of all simple modules, and gave some related applications.

Key words: , semiprimary ring, Gorenstein projective module, , X-Gorenstein projective module, X-Gorenstein (global) , projective dimension

中图分类号:

O154.2

赵志兵. 半准素环的X-Gorenstein整体投射维数[J]. 吉林大学学报(理学版), 2018, 56(5): 1136-1139.

ZHAO Zhibing. Gorenstein Global Projective Dimension of Semiprimary Rings[J]. Journal of Jilin University Science Edition, 2018, 56(5): 1136-1139.