On von Neumann regular rings with weak comparability

In 1991, K.C. OʹMeara first defined the notion of weak comparability for regular rings, and he showed that every simple directly finite regular ring with weak comparability is unit-regular. In this paper, we investigate properties for regular rings with weak comparability, and we show that the strict cancellation property and the strict unperforation property hold for the family of directly finite finitely generated projective modules over these rings.