Article contents
TWO QUESTIONS OF L. VAŠ ON
$\ast $-CLEAN RINGS
Published online by Cambridge University Press: 08 March 2013
Abstract
A $\ast $-ring
$R$ is called (strongly)
$\ast $-clean if every element of
$R$ is the sum of a unit and a projection (that commute). Vaš [‘
$\ast $-Clean rings; some clean and almost clean Baer
$\ast $-rings and von Neumann algebras’, J. Algebra 324(12) (2010), 3388–3400] asked whether there exists a
$\ast $-ring that is clean but not
$\ast $-clean and whether a unit regular and
$\ast $-regular ring is strongly
$\ast $-clean. In this paper, we answer these two questions. We also give some characterisations related to
$\ast $-regular rings.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 88 , Issue 3 , December 2013 , pp. 499 - 505
- Copyright
- Copyright ©2013 Australian Mathematical Publishing Association Inc.
References
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