JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Previous Articles     Next Articles

WGP-injectivity of rings#br#

LU Qi1, BAO Hong-wei1, LIANG Liang2   

  1. 1. Department of Mathematics and Physics, Bengbu College, Bengbu 233030, Anhui, China;
    2. School of Mathematical Science, Yangzhou University, Yangzhou 225002, Jiangsu, China
  • Received:2013-09-25 Online:2014-06-20 Published:2014-06-14

PDF (PC)

629

Abstract: Some equivalent definitions of WGP-injective rings are introduced. And the properties of WGP-injective rings are studied. It is proved that if R is a left nonsingular left WGP-injective ring, and the ascending chain l(a1)l(a1a2)l(a1a2a3)… terminates for every infinite sequence a1,a2,a3…, then R is semisimple.

Key words: GP-injective ring, WGP-injective ring, von-Neumann regular ring, semisimple ring

[1] CHEN Dong, WANG Fang-gui, JIAN Hong, CHEN Ming-zhao. Structure of modules over 2-strongly Gorenstein semisimple ring with its application [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 24-30.
[2] LU Qi, BAO Hong-wei. ZWGP-injectivity and nonsingularity of rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 19-23.
[3] LU Qi, YIN Xiao-bin, BAO Hong-wei. EP-injectivity and von Neumann regularity of rings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 33-37.
[4] YIN Xiao-bin1, HUANG Xiao-lin1, WANG Kai-yun2. Endomorphism rings of quasi AP-injective modules [J]. J4, 2010, 45(6): 31-34.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd