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On strongly pi-regular rings of stable range one

Published online by Cambridge University Press:  17 April 2009

Hua-Ping Yu  and
Victor P. Camilo
Hua-Ping Yu
Affiliation:
Department of Mathematics, The University of Iowa, Iowa City IA 52242, United States of America, e-mail: hpyu@math.uiowa.edu
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Abstract

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An associative ring R is said to have stable range one if for any a, b ∈ R satisfying aR + bR = R, there exists y ∈ R such that a + by is right (equivalently, left) invertible. Call a ring R strongly π-regular if for every element a ∈ R there exist a number n (depending on a) and an element x ∈ R such that an = an+1x. It is an open question whether all strongly π-regular rings have stable range one. The purpose of this note is to prove the following Theorem: If R is a strongly π-regular ring with the property that all powers of every nilpotent von Neumann regular element are von Neumann regular in R, then R has stable range one.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 3 , June 1995 , pp. 433 - 437
Copyright
Copyright © Australian Mathematical Society 1995

References

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