• 제목/요약/키워드: simple singular modules

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A NOTE ON SIMPLE SINGULAR GP-INJECTIVE MODULES

  • Nam, Sang Bok
    • Korean Journal of Mathematics
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    • 제7권2호
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    • pp.215-218
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    • 1999
  • We investigate characterizations of rings whose simple singular right R-modules are GP-injective. It is proved that if R is a semiprime ring whose simple singular right R-modules are GP-injective, then the center $Z(R)$ of R is a von Neumann regular ring. We consider the condition ($^*$): R satisfies $l(a){\subseteq}r(a)$ for any $a{\in}R$. Also it is shown that if R satisfies ($^*$) and every simple singular right R-module is GP-injective, then R is a reduced weakly regular ring.

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MC2 Rings

  • Wei, Jun-Chao
    • Kyungpook Mathematical Journal
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    • 제48권4호
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    • pp.651-663
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    • 2008
  • In this paper, we first study some characterizations of left MC2 rings. Next, by introducing left nil-injective modules, we discuss and generalize some well known results for a ring whose simple singular left modules are Y J-injective. Finally, as a byproduct of these results we are able to show that if R is a left MC2 left Goldie ring whose every simple singular left R-module is nil-injective and GJcp-injective, then R is a finite product of simple left Goldie rings.

ON RINGS WHOSE PRIME IDEALS ARE MAXIMAL

  • Hong, Chan-Yong;Kim, Nam-Kyun;Kwak, Tai-Keun
    • 대한수학회보
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    • 제37권1호
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    • pp.1-19
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    • 2000
  • We investigate in this paper the maximality of prime ideals in rings whose simple singular left R-modules are p-injective.

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Rings Whose Simple Singular Modules are PS-Injective

  • Xiang, Yueming;Ouyang, Lunqun
    • Kyungpook Mathematical Journal
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    • 제54권3호
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    • pp.471-476
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    • 2014
  • Let R be a ring. A right R-module M is PS-injective if every R-homomorphism $f:aR{\rightarrow}M$ for every principally small right ideal aR can be extended to $R{\rightarrow}M$. We investigate, in this paper, rings whose simple singular modules are PS-injective. New characterizations of semiprimitive rings and semisimple Artinian rings are given.

A Note on GQ-injectivity

  • Kim, Jin-Yong
    • Kyungpook Mathematical Journal
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    • 제49권2호
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    • pp.389-392
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    • 2009
  • 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.