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Stable Range One for Rings with Many Idempotents
Journal article   Open access   Peer reviewed

Stable Range One for Rings with Many Idempotents

Victor P. Camillo and Hua-Ping Yu
Transactions of the American Mathematical Society, Vol.347(8), pp.3141-3147
08/01/1995
DOI: 10.2307/2154778
url
https://doi.org/10.2307/2154778View
Published (Version of record) Open Access

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].
Mathematics Physical Sciences Science & Technology

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