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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

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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

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