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A Note on GQ-injectivity
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  • Journal title : Kyungpook mathematical journal
  • Volume 49, Issue 2,  2009, pp.389-392
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2009.49.2.389
 Title & Authors
A Note on GQ-injectivity
Kim, Jin-Yong;
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The purpose of this note is to improve several known results on GQ-injective rings. We investigate in this paper the von Neumann regularity of left GQ-injective rings. We give an answer a question of Ming in the positive. Actually it is proved that if R is a left GQ-injective ring whose simple singular left R-modules are GP-injective then R is a von Neumann regular ring.
GP-injevtive modules;GQ-injective rings;von Neumann regular rings;idempotent reflexive rings;
 Cited by
J. Chen and N. N. Ding, On regularity of rings, Algebra Colloq., 8(2001), 267-274.

J. Chen, Y. Zhou and Z. Zhu, GP-injective Rings need not be P-injective, Comm. in Algebra, 32(2004), 1-9. crossref(new window)

Y. Hirano, H. K. Kim and J. Y. Kim, A note on GP-injectivity, to appear in Algebra Colloq.

J. Y. Kim, Certain rings whose simple singular modules are GP-injective, Proc. of Japan Academy, 81(2005), 125-128. crossref(new window)

R. Y. C. Ming, On quasi-injectivity and von Neumann regularity, Mh. Math., 95(1983), 25-32. crossref(new window)

R. Y. C. Ming, On YJ-injectivity and VNR rings, Bull. Math. Soc. Sc. Math. Roumanie Tome, 46(94)(2003), 87-97.

R. Y. C. Ming, A note on P-injectivity, Demonstratio Mathematica, 37(2004), 45-54.

R. Y. C. Ming, On YJ-injectivity and Annihilators, Georgian Mathematical Journal, 12(2005), 573-581.

Y. Utumi, On continuous rings and self-injective rings, Trans. Amer. Math. Soc. 118(1965), 158-173. crossref(new window)