Stable range one for rings with many idempotents

Authors:
Victor P. Camillo and Hua-Ping Yu

Journal:
Trans. Amer. Math. Soc. **347** (1995), 3141-3147

MSC:
Primary 16D70; Secondary 16U50, 19B10

DOI:
https://doi.org/10.1090/S0002-9947-1995-1277100-2

MathSciNet review:
1277100

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Abstract | References | Similar Articles | Additional Information

Abstract: An associative ring is said to have stable range if for any , satisfying , there exists such that by is a unit. The purpose of this note is to prove the following facts. Theorem : An exchange ring has stable range if and only if every regular element of is unit-regular. Theorem : If is a strongly -regular ring with the property that all powers of every regular element are regular, then has stable range . The latter generalizes a recent result of Goodearl and Menal [].

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1277100-2

Keywords:
Stable range one,
exchange ring,
strongly -regular ring

Article copyright:
© Copyright 1995
American Mathematical Society