2009/02/07 by Kabbour, Mohammed, Mahdou, Najib
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.0902.1236
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∝ 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.