On Regular Rings Satisfying Almost Comparability

Abstract

In this article, we study regular rings satisfying almost comparability. We first show that, for regular rings, almost comparability is inherited by finitely generated projective modules and finite matrix rings, and, as a main result, we prove that the strict cancellation property holds for the family of all finitely generated projective modules over directly finite regular rings satisfying almost comparability.

Key Words:

• Almost comparability
• Strict cancellation
• Von Neumann regular rings

Mathematics Subject Classification (2000):

• 16E50
• 16D70

ACKNOWLEDGMENT

The author expresses his gratitude to the referee for many useful comments on this article.

Notes

Communicated by R. Wisbauer.