Abstract
All rings considered in this letter are associative with identity, and all modules areunital. A ring R is von Neumann regular provided that for every a∈R there exists b∈Rsuch that a=aba. R is called a strongly regular ring if for each a∈R, a∈a~2R. Recall thatR is MELT (resp. ELT) if every maximal essential (resp. essential) left ideal of R is anideal of R. As usual, R is called a right (left) V-ring if every simple right (left) R-moduleis injective. For several years, the connections between von Neumann regular rings and re-
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