JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (4): 46-53.doi: 10.6040/j.issn.1671-9352.0.2020.521

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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

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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

CLC Number: 

  • O153.3
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[1] CHEN Ling-qiao, TANG Gou-liang, DI Zhen-xing. Equivalent characterization of(strong)Kasch triangular matrix ring of order n [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(4): 25-30.
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