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Almost Abelian rings

Junchao Wei (2013)

Communications in Mathematics

A ring R is defined to be left almost Abelian if a e = 0 implies a R e = 0 for a N ( R ) and e E ( R ) , where E ( R ) and N ( R ) stand respectively for the set of idempotents and the set of nilpotents of R . Some characterizations and properties of such rings are included. It follows that if R is a left almost Abelian ring, then R is π -regular if and only if N ( R ) is an ideal of R and R / N ( R ) is regular. Moreover it is proved that (1) R is an Abelian ring if and only if R is a left almost Abelian left idempotent reflexive ring. (2) R is strongly...

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