您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (8): 75-79.doi: 10.6040/j.issn.1671-9352.0.2019.538

• • 上一篇    

单Utumi模

吴德军,卢锐涛,王永铎*   

  1. 兰州理工大学理学院, 甘肃 兰州 730050
  • 发布日期:2020-07-14
  • 作者简介:吴德军(1978— ),男,博士,副教授,研究方向为同调代数及表示论. E-mail: wudj@lut.cn*通信作者简介:王永铎(1974— ),男,博士,教授,研究方向为环与模范畴. E-mail: ydwang@lut.cn
  • 基金资助:
    国家自然科学基金资助项目(11761047;11861043)

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

摘要: 引入了单Utumi模和奇异单Utumi模的概念, 研究了它们的基本性质, 证明了环R是右V-环当且仅当每个右R-模是单Utumi模; R是右GV-环当且仅当每个右R-模是奇异单Utumi模; R是半单阿廷环当且仅当每个单Utumi右R-模是内射模

关键词: 单Utumi模, 奇异单Utumi模, V-环, GV-环

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

中图分类号: 

  • O152.7
[1] IBRAHIM Y, YOUSIF M. Utumi modules[J]. Communications in Algebra, 2018, 46(2): 870-886.
[2] CAMILLO V, IBRAHIM Y, YOUSIF M, et al. Simple-direct-injective modules[J]. Journal of Algebra, 2014, 420: 39-53.
[3] WANG Y D. Simple continuous modules[J]. Hacettepe Journal of Mathematics and Statistics, 2018, 48(5). doi:10.15672/hjms.2018.565.
[4] RAMAMURTHI V S, RANGASWAMY K M. Generalized V-rings[J]. Mathematica Scandinavica, 1972, 31: 69-72.
[5] MAZUREK R, NIELSEN P P, ZIEMBOWSKI M. Commuting idempotents, square-free modules, and the exchange property[J]. Journal of Algebra, 2015, 444: 52-80.
[6] ÖZCAN A Ç, HARMANCI A, SMITH P F. Duo modules[J]. Glasgow Mathematical Journal, 2006, 48(3): 533-545.
[7] SMITH P F. Modules for which every submodule has a unique closure [M] //Ring Theory. Singapore: Word Scientific, 1993:303-313.
[8] MOHAMED S H, MÜLLER B J. Continuous and discrete modules[M] // Cambridge: Cambridge University Press, 1990.
[9] AMIN I, YOUSIF M, ZEYADA N. Soc-injective rings and modules[J]. Communications in Algebra, 2005, 33(11): 4229-4250.
[10] LAM T Y. Lectures on modules and rings [M]. New York: Springer-Verlag, 1999.
[1] 王永铎,马亚军. 单dual Rickart模[J]. 山东大学学报(理学版), 2017, 52(12): 5-9.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!