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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (4): 46-53.doi: 10.6040/j.issn.1671-9352.0.2020.521

• • 上一篇    

n阶三角矩阵环上的有限嵌入模

孙博,殷玉洁,狄振兴*   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 发布日期:2021-04-13
  • 作者简介:孙博(1997— ), 男, 硕士研究生, 研究方向为环的同调理论. E-mail:sunbo9797@126.com*通信作者简介:狄振兴(1984— ), 男, 博士, 副教授, 博士研究生导师, 研究方向为环的同调理论与代数表示理论. E-mail:dizhenxing19841111@126.com
  • 基金资助:
    国家自然科学基金资助项目(11971388)

Finitely embedded modules over triangular matrix rings of order n

SUN Bo, YIN Yu-jie, DI Zhen-xing*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2021-04-13

摘要: 设Γ是一个n阶三角矩阵环,其中n≥2是一个整数。给出了一个Γ-模的子模是本质子模的等价刻画与一个Γ-模的基座具体形式。特别地,作为上述结论的运用,给出了一个Γ-模是有限嵌入模的充分必要条件。

关键词: n阶三角矩阵环, 本质子模, 基座, 有限嵌入模

Abstract: Let Γ be a triangular matrix ring of order n, where n≥2 is an integer. The equivalent characterization of a Γ-module whose submodule is an essential submodule, and the concrete description of the socle of a Γ-module are given. In particular, as an application of the above conclusion, a necessary and sufficient condition for a Γ-module to be a finitely embedded module is given.

Key words: triangular matrix ring of order n, essential submodule, socle, finitely embedded module

中图分类号: 

  • O153.3
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[1] 陈玲巧,唐国亮,狄振兴. (强)Kasch n阶三角矩阵环的等价刻画[J]. 《山东大学学报(理学版)》, 2021, 56(4): 25-30.
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