形式三角矩阵环上的 Gorenstein FP-内射模

doi:10.6040/j.issn.1671-9352.0.2021.328

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (2): 38-44.doi: 10.6040/j.issn.1671-9352.0.2021.328

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形式三角矩阵环上的 Gorenstein FP-内射模

杨银银,张翠萍^*

西北师范大学数学与统计学院, 甘肃兰州 730070

发布日期:2022-01-07
作者简介:杨银银(1996— ), 女, 硕士研究生, 研究方向为环的同调理论. E-mail:1739238198@qq.com*通信作者简介:张翠萍(1974— ), 女, 博士, 副教授, 硕士生导师, 研究方向为环的同调理论. E-mail:zhangcp@nwnu.edu.cu
基金资助:
国家自然科学基金资助项目(11761060)

Gorenstein FP-injective modules over formal triangular matrix rings

YANG Yin-yin, ZHANG Cui-ping^*

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Published:2022-01-07

摘要/Abstract

摘要： 设T=(A 0U B)是形式三角矩阵环,其中A,B是环,U是(B,A)-双模。证明了若T是左凝聚环,_BU是有限表示的且pd(_BU)<∞, M=(M₁M₂)_φ^M是Gorenstein FP-内射左T-模,则 Ker φ^M^~是Gorenstein FP-内射左A-模,M₂是Gorenstein FP-内射左B-模,且φ^M^~是满同态;若T还是左GFPI-封闭环,则反之成立。

关键词: 形式三角矩阵环, FP-内射模, Gorenstein FP-内射模

Abstract: Let T=(A 0U B) be a formal triangular matrix ring, where A and B are rings and U is (B,A)-bimodule. It is proved that if T is a left cocherent ring, _BU is finitely presented and pd(_BU)<∞, M=(M1M2)_φ^M is Gorenstein FP-injective left T-module, then Ker φ^M^~ is Gorenstein FP-injective left A-module, M2 is Gorenstein FP-injective left B-module, and φ^M^~ is an epimorphism; if T is still a left GFPI-closed ring, then the opposite case holds.

Key words: formal triangular matrix ring, FP-injective module, Gorenstein FP-injective module

中图分类号:

O153.3

杨银银,张翠萍. 形式三角矩阵环上的 Gorenstein FP-内射模[J]. 《山东大学学报(理学版)》, 2022, 57(2): 38-44.

YANG Yin-yin, ZHANG Cui-ping. Gorenstein FP-injective modules over formal triangular matrix rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(2): 38-44.

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形式三角矩阵环上的 Gorenstein FP-内射模

Gorenstein FP-injective modules over formal triangular matrix rings

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