On π-regularity of General Rings |
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作者单位: | School of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai, 264005 |
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基金项目: | The NSF (Y2008A04) of Shandong Province of China |
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摘 要: | A general ring means an associative ring with or without identity.An idempotent e in a general ring I is called left (right) semicentral if for every x ∈ I,xe=exe (ex=exe).And I is called semiabelian if every idempotent in I is left or right semicentral.It is proved that a semiabelian general ring I is π-regular if and only if the set N (I) of nilpotent elements in I is an ideal of I and I /N (I) is regular.It follows that if I is a semiabelian general ring and K is an ideal of I,then I is π-regular if and only if both K and I /K are π-regular.Based on this we prove that every semiabelian GVNL-ring is an SGVNL-ring.These generalize several known results on the relevant subject.Furthermore we give a characterization of a semiabelian GVNL-ring.
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关 键 词: | EXE文件 exe文件 结合环 零元素 幂等 证明 理想 L环 |
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