JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (8): 75-79.doi: 10.6040/j.issn.1671-9352.0.2019.538

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Simple Utumi modules

WU De-jun, LU Rui-tao, WANG Yong-duo*   

  1. School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, China
  • Published:2020-07-14

Abstract: Simple Utumi modules and singular simple Utumi modules are introduced, and their fundamental properties are studied. It is proved that a ring R is a right V-ring if and only if each right R-module is a simple Utumi module, a ring R is a right GV-ring if and only if each right R-module is a singular simple Utumi module and a ring R is a semisimple Artinian ring if and only if each simple Utumi right R-module is an injective module.

Key words: simple Utumi module, singular simple Utumi module, V-ring, GV-ring

CLC Number: 

  • O152.7
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