挠理论中的相对内射模

数学季刊 ›› 2007, Vol. 22 ›› Issue (4): 500-503.

挠理论中的相对内射模

1.College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000,China;2.Department of Mathematics, Southeast University, Nangjing 210096,China

收稿日期:2005-06-15 出版日期:2007-12-30 发布日期:2023-10-19
作者简介: SONG Xian-mei(1977-), female, native of Xuzhou, Jiangsu, a lecturer of Anhui Normal Univer- sity, Ph.D., engages in ring theory and homological algebra.
基金资助:
Supported by the National Natural Science Foundation of China(10571026)； Supported by the Research Foundation of the Education Committee of Anhui Province(2006kj050c)； Supported by the Doctoral Foundation of Anhui Normal University；

Relatively Injective Modules with Respect to Torsion Theory

1.College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000,China;2.Department of Mathematics, Southeast University, Nangjing 210096,China

Received:2005-06-15 Online:2007-12-30 Published:2023-10-19
About author: SONG Xian-mei(1977-), female, native of Xuzhou, Jiangsu, a lecturer of Anhui Normal Univer- sity, Ph.D., engages in ring theory and homological algebra.
Supported by:
Supported by the National Natural Science Foundation of China(10571026)； Supported by the Research Foundation of the Education Committee of Anhui Province(2006kj050c)； Supported by the Doctoral Foundation of Anhui Normal University；

摘要/Abstract

摘要： For a hereditary torsion theory T,this paper mainly discuss properties of A_-τ- injective modules,where A is a fixed left R-module.It is proved that if M is an A_-τ-injective, B is a submodule of A,then 1)M is A/B-τ-injective;2)M is B_-τ-injective when B isτ- dense in A.Furthermore,we show that if A₁,A_2,…,A_n are relatively injective modules, then A₁⊕A₂⊕…⊕A_n is self-τ-injective if and only if A_{i i}s self_-τ-injective for each i.

关键词: hereditary torsion theory, T-dense submodule, A_-T-injective module

Abstract: For a hereditary torsion theory T,this paper mainly discuss properties of A_-τ- injective modules,where A is a fixed left R-module.It is proved that if M is an A_-τ-injective, B is a submodule of A,then 1)M is A/B-τ-injective;2)M is B_-τ-injective when B isτ- dense in A.Furthermore,we show that if A₁,A_2,…,A_n are relatively injective modules, then A₁⊕A₂⊕…⊕A_n is self-τ-injective if and only if A_{i i}s self_-τ-injective for each i.

Key words: hereditary torsion theory, T-dense submodule, A_-T-injective module

中图分类号:

O153

宋贤梅, 陈建龙. 挠理论中的相对内射模[J]. 数学季刊, 2007, 22(4): 500-503.

SONG Xian-mei, CHEN Jian-long. Relatively Injective Modules with Respect to Torsion Theory[J]. Chinese Quarterly Journal of Mathematics, 2007, 22(4): 500-503.

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