Journal article
Stable Range One for Rings with Many Idempotents
Transactions of the American Mathematical Society, Vol.347(8), pp.3141-3147
08/01/1995
DOI: 10.2307/2154778
Abstract
An associative ring R is said to have stable range 1 if for any a, b is an element of R satisfying aR + bR = R, there exists y is an element of R such that a + by is a unit. The purpose of this note is to prove the following facts. Theorem 3: An exchange ring R has stable range 1 if and only if every regular element of R is unit-regular. Theorem 5: If R is a strongly pi-regular ring with the property that all powers of every regular element are regular, then R has stable range 1. The latter generalizes a recent result of Goodearl and Menal [5].
Details
- Title: Subtitle
- Stable Range One for Rings with Many Idempotents
- Creators
- Victor P. Camillo - University of Iowa, MathematicsHua-Ping Yu - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Transactions of the American Mathematical Society, Vol.347(8), pp.3141-3147
- DOI
- 10.2307/2154778
- ISSN
- 0002-9947
- Publisher
- American Mathematical Society
- Number of pages
- 7
- Language
- English
- Date published
- 08/01/1995
- Academic Unit
- Mathematics
- Record Identifier
- 9983985869302771
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