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Acta Mathematica Vietnamica

SOME NOTES ON WEAKLY REVERSIBLE RINGS

icon-email JUNCHAO WEI

Abstract

In this paper, we give some properties of weakly reversible rings, such as weakly reversible rings are left min-abel and directly finite. Next, we show that R is a strongly regular ring if and only if R is a weakly reversible regular ring. Finally, we give some applications: Let R be a weakly reversible ring. Then (1) R is clean if and only if R is exchange; (2) If R is exchange, then R has stable range one; (3) If R is a clean ring, then R is a tb-ring.