A Note on GQ-injectivity
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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.
Abstract
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.
참고문헌 (9)
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- J. Chen, "GP-injective Rings need not be P-injective", Comm. in Algebra, 32, pp.1~9 (2004)
- Y. Hirano, "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, pp.125~128 (2005)
- R. Y. C. Ming, "On quasi-injectivity and von Neumann regularity", Mh. Math, 95, pp.25~32 (1983)
- R. Y. C. Ming, "On YJ-injectivity and VNR rings", Bull. Math. Soc. Sc. Math. Roumanie Tome, 46(94), pp.87~97 (2003)
- R. Y. C. Ming, "A note on P-injectivity", Demonstratio Mathematica, 37, pp.45~54 (2004)
- R. Y. C. Ming, "On YJ-injectivity and Annihilators", Georgian Mathematical Journal, 12, pp.573~581 (2005)
- Y. Utumi, "On continuous rings and self-injective rings", Trans. Amer. Math. Soc, 118, pp.158~173 (1965)