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On π-regularity of General Rings
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作者 CHEN WEI-XING CUI SHU-YING 《Communications in Mathematical Research》 CSCD 2010年第4期313-320,共8页
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 idempot... 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. 展开更多
关键词 semiabelian ring π-regular ring GVNL-ring exchange ring
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拟AP-内射模的自同态环 被引量:1
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作者 殷晓斌 黄晓林 汪开云 《山东大学学报(理学版)》 CAS CSCD 北大核心 2010年第6期31-34,共4页
设R为环,MR是拟AP-内射模,S=End(MR), N(S)表示S的幂零元之集。研究了满足升链条件的环S的强正则性和半单性以及与一些特殊环的关系。
关键词 拟AP-内射模 特殊的升链条件 强正则环 半单环 半阿贝尔环
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