Acta mathematica scientia,Series A

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On Projectives over Radical Total Rings

Feng Lianggui; Piao Zhihui   

  1. Department of Mathematics and System Science, National University of Defense Technology, Changsha 410073
  • Received:2005-12-15 Revised:2006-09-22 Online:2007-06-25 Published:2007-06-25
  • Contact: Feng Lianggui

Abstract: The decomposition theorems on projective modules over radical total rings are built in this paper. For a total free ring $R$ with $u.{\rm dim}_{R}R < \infty$, it is showed that $R$ is Noetherian with gldim$R \leqslant 1$, and any projective module $P$ over $R$ is isomorphic to $ \bigoplus\limits_{i\in
I}Re_{i}$, in which each $e_{i}$ is a nonzero idempotent in $R$.
Some examples are also given.

Key words: Radicaltotal ring, Decomposition, Total, Idempotent

CLC Number: 

  • 16E50
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