广义P-平坦性和广义P-内射性的一些刻画

吉林大学学报(理学版)

广义P-平坦性和广义P-内射性的一些刻画

王修建^1,2, 杜先能²

1. 皖西学院应用数学学院, 安徽六安 237012; 2. 安徽大学数学科学学院, 合肥 230600

收稿日期:2012-11-26 出版日期:2013-07-26 发布日期:2013-08-06
通讯作者: 杜先能 E-mail:xndu@ahu.edu.cn

Some Characterizations on Generalized PFlatness and P-Injectivity

WANG Xiujian^1,2, DU Xianneng²

1. School of Applied Mathematics, West Anhui University, Lu’an 237012, Anhui Province, China;2. School of Mathematics Sciences, Anhui University, Hefei 230600, China

Received:2012-11-26 Online:2013-07-26 Published:2013-08-06
Contact: DU Xianneng E-mail:xndu@ahu.edu.cn

摘要/Abstract

摘要：

利用同调代数方法分别给出了环R为左GP-内射环、左GPP-环和左GPF-环的一些等价刻画, 通过引入GP-内射维数和GP-平坦维数的概念, 证明了在左P-凝聚环条件下, 环的左GP-内射整体维数等于环的右GP-弱维数, 并给出了GP-内射维数和GP-平坦维数的若干新刻画.

关键词: GP-平坦模, GP-内射模, GP-平坦维数, GP-内射维数

Abstract:

By means of homological algebra, some equivalent characterizations were given when R was left GP-injective ring, left GPP-ring or left GPF-ring. Having introduced the notions of GP-injective dimensions and GP-flat dimensions, we proved that left GP-injective global dimension is equal to right GP-weak dimension of R under the condition that R is left P-coherent. Furthermore, some new characterizations of GP-injective dimensions and GP-flat dimensions were also given.

Key words: GP-flat module, GP-injective module, GP-flat dimension； GP-injective dimension

中图分类号:

O153.3

王修建, 杜先能. 广义P-平坦性和广义P-内射性的一些刻画[J]. 吉林大学学报(理学版), 2013, 51(04): 608-612.

WANG Xiujian, DU Xianneng. Some Characterizations on Generalized PFlatness and P-Injectivity[J]. Journal of Jilin University Science Edition, 2013, 51(04): 608-612.