On Von Neumann Regular Rings With Weak Comparability II

ABSTRACT

O'Meara (1991) first gave the notion of weak comparability for regular rings, to prove that every simple directly finite regular ring with weak comparability is unit-regular. In this article, 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 all nonzero finitely generated projective modules over these rings. Also, we show that weak comparability for regular rings is Morita invariant.

Keywords:

• S-comparability
• Strict unperforation
• Von Neumann regular rings
• Weak comparability

Mathematics Subject Classification (2000):

• 16E50
• 16D70

ACKNOWLEDGMENT

The author expresses his gratitude to the referee for many useful suggestions on the first version of this paper.

Notes

^#Communicated by R. Wisbauer.