三角矩阵环上Gorenstein FP-内射模的刻画

doi:10.6040/j.issn.1671-9352.0.2021.062

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (8): 86-93.doi: 10.6040/j.issn.1671-9352.0.2021.062

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三角矩阵环上Gorenstein FP-内射模的刻画

吴德军,周慧^*

兰州理工大学理学院, 甘肃兰州 730050

发布日期:2021-08-09
作者简介:吴德军(1978— ), 男, 博士,教授, 研究方向为同调代数. E-mail:wudj@lut.edu.cn*通信作者简介:周慧(1997— ), 女, 硕士, 研究方向为同调代数. E-mail:2536721009@qq.com
基金资助:
国家自然科学基金资助项目(11761047)

A characterization of Gorenstein FP-injective modules over triangular matrix rings

WU De-jun, ZHOU Hui^*

School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, China

Published:2021-08-09

摘要/Abstract

摘要： 设T=(A 0U B)是形式三角矩阵环, 给出了Gorenstein FP-内射左T-模的一个等价刻画。

关键词: Gorenstein FP-内射模, 左凝聚环, 形式三角矩阵环

Abstract: Let T=(A 0U B) be a formal triangular matrix ring. A characterization of Gorenstein FP-injective left T-modules is given.

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

中图分类号:

O154.2

吴德军,周慧. 三角矩阵环上Gorenstein FP-内射模的刻画[J]. 《山东大学学报(理学版)》, 2021, 56(8): 86-93.

WU De-jun, ZHOU Hui. A characterization of Gorenstein FP-injective modules over triangular matrix rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(8): 86-93.

[1] MAO Lixin, DING Nanqing. Gorenstein FP-injective and Gorenstein flat modules[J]. Journal of Algebra and Its Applications, 2008, 7(4):491-506.
[2] XIN Dawei, CHEN Jianlong, ZHANG Xiaoxiang. On Gorenstein FP-injective and Gorenstein flat complexes[J]. Communications in Algebra, 2013, 41(4):1247-1267.
[3] YANG Chunhua. Strongly Gorenstein flat and Gorenstein FP-injective modules[J]. Turkish Journal of Mathematics, 2013, 37(2):218-230.
[4] SELVARAJ C, SARAVANAN R. Gorenstein n-FP-injective and Gorenstein n-flat complexes[J]. Bollettino dellUnione Matematica Italiana, 2016, 11(2):147-161.
[5] ENOCHS E E, CORTÉS-IZURDIAGA M, TORRECILLAS B. Gorenstein conditions over triangular matrix rings[J]. Journal of Pure and Applied Algebra, 2014, 218(8):1544-1554.
[6] MAO Lixin. Duality pairs and FP-injective modules over formal triangular matrix rings[J]. Communications in Algebra, 2020, 48(12):5296-5310.
[7] 佟文廷. 同调代数引论[M]. 北京: 高等教育出版社, 1998. TONG Wenting. An Introduction to Homological Algebra[M]. Beijing: Higher Education Press, 1998.
[8] GAO Zenghui, WANG Fanggui. Coherent rings and Gorenstein FP-injective modules[J]. Communications in Algebra, 2012, 40(5):1532-4125.

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三角矩阵环上Gorenstein FP-内射模的刻画

A characterization of Gorenstein FP-injective modules over triangular matrix rings

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