Displaying similar documents to “On regular endomorphism rings of topological Abelian groups”

The almost isomorphism relation for simple regular rings.

Pere Ara, Kenneth R. Goodearl (1992)

Publicacions Matemàtiques

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A longstanding open problem in the theory of von Neumann regular rings is the question of whether every directly finite simple regular ring must be unit-regular. Recent work on this problem has been done by P. Menal, K. C. O'Meara, and the authors. To clarify some aspects of these new developments, we introduce and study the notion of almost isomorphism between finitely generated projective modules over a simple regular ring.

Almost Abelian rings

Junchao Wei (2013)

Communications in Mathematics

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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 ...