形式三角矩阵环上的强Ding投射模和强Ding内射模

doi:10.6040/j.issn.1671-9352.0.2020.032

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (10): 37-45.doi: 10.6040/j.issn.1671-9352.0.2020.032

形式三角矩阵环上的强Ding投射模和强Ding内射模

赵阳,张文汇^*

西北师范大学数学与统计学院, 甘肃兰州 730070

出版日期:2020-10-20 发布日期:2020-10-07
作者简介:赵阳(1995— ), 女, 硕士研究生, 研究方向为环的同调理论. E-mail:1623089534@qq.com*通信作者简介:张文汇(1977— ), 女, 博士, 副教授, 硕士研究生导师, 研究方向为环的同调理论. E-mail:zhangwh@nwnu.edu.cn
基金资助:
国家自然科学基金资助项目(11861055)

Strongly Ding projective and strongly Ding injective modules over formal triangular matrix rings

ZHAO Yang, ZHANG Wen-hui^*

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

Online:2020-10-20 Published:2020-10-07

摘要/Abstract

摘要： 讨论了形式下三角矩阵环T=(A 0U B)上的强Ding投射模和强Ding内射模,证明了当U_A和_BU的平坦维数有限,并且(M₁M₂)_φ^M是强Ding投射左T-模时,M₁是强Ding投射左A-模,φ^M是单同态,M₂/Im φ^M是强Ding投射左B-模。

关键词: 形式三角矩阵环, 强Ding投射模, 强Ding内射模

Abstract: Strongly Ding projective and strongly Ding injective modules are investigated over the formal triangular matrix ring T=(A 0U B). It is proved that if both U_A and _BU have finite flat dimensions, and left T-module (M1M2)_φ^M is strong Ding projective, left A-module M₁ is strong Ding projective, φ^M is a monomorphism, left B-module M2/Im φ^M is strong Ding projective.

Key words: formal triangular matrix ring, strongly Ding projective module, strongly Ding injective module

中图分类号:

O153.3

赵阳,张文汇. 形式三角矩阵环上的强Ding投射模和强Ding内射模[J]. 《山东大学学报(理学版)》, 2020, 55(10): 37-45.

ZHAO Yang, ZHANG Wen-hui. Strongly Ding projective and strongly Ding injective modules over formal triangular matrix rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 37-45.

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形式三角矩阵环上的强Ding投射模和强Ding内射模

Strongly Ding projective and strongly Ding injective modules over formal triangular matrix rings

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