Abstract
The notion of weak comparability was first introduced by K.C. O’Meara, to prove that directly finite simple regular rings satisfying weak comparability must be unit-regular. In this paper, we shall treat (non-necessarily simple) regular rings satisfying weak comparability and give some interesting results. We first show that directly finite regular rings satisfying weak comparability are stably finite. Using the result above, we investigate the strict cancellation property and the strict unperforation property for regular rings satisfying weak comparability, and we show that these rings have the strict unperforation property, which means that nA ≺ nB implies A ≺ B for any finitely generated projective modules A, B and any positive integer n.
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Kutami, M. Von Neumann Regular Rings Satisfying Weak Comparability. Appl Categor Struct 16, 183–194 (2008). https://doi.org/10.1007/s10485-006-9056-1
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DOI: https://doi.org/10.1007/s10485-006-9056-1