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《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

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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*   

  1. 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*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Online:2020-10-20 Published:2020-10-07

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UABU的平坦维数有限,并且(M1M2)φM是强Ding投射左T-模时,M1是强Ding投射左A-模,φM是单同态,M2/Im φM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 UA and BU have finite flat dimensions, and left T-module (M1M2)φM is strong Ding projective, left A-module M1 is strong Ding projective, φM is a monomorphism, left B-module M2/Im φM 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
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