On Weakly von Neumann regular rings

Details On Weakly von Neumann regular rings On Weakly von Neumann regular rings

2009-02-07

arxiv.org/abs/0902.1236v3

Mathematics

Commutative Algebra

Scientific paper

In this paper, we define and study a particular case of von Neumann regular notion called a weak von Neumann regular ring. It shown that the polynomial ring $R[x]$ is weak von Neumann regular if and only if $R$ has exactly two idempotent elements. We provide necessary and sufficient conditions for $ R=A\propto E $ to be a weak von Neumann ring. It is also shown that $I$ is a primary ideal imply $R/I$ is a weak von Neumann regular ring.

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