### 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.

CLC Number:

• 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] WANG Yong-duo, MA Ya-jun. Simple dual Rickart modules [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 5-9.
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