2 results
ON CLEAN LAURENT SERIES RINGS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 95 / Issue 3 / December 2013
- Published online by Cambridge University Press:
- 18 July 2013, pp. 421-427
- Print publication:
- December 2013
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- Article
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Here we prove that, for a
$2$-primal ring 
$R$, the Laurent series ring 
$R((x))$ is a clean ring if and only if 
$R$ is a semiregular ring with 
$J(R)$ nil. This disproves the claim in K. I. Sonin [‘Semiprime and semiperfect rings of Laurent series’, Math. Notes 60 (1996), 222–226] that the Laurent series ring over a clean ring is again clean. As an application of the result, it is shown that, for a 
$2$-primal ring 
$R$, 
$R((x))$ is semiperfect if and only if 
$R((x))$ is semiregular if and only if 
$R$ is semiperfect with 
$J(R)$ nil.
ON KRULL–SCHMIDT FINITELY ACCESSIBLE CATEGORIES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 84 / Issue 1 / August 2011
- Published online by Cambridge University Press:
- 01 April 2011, pp. 90-97
- Print publication:
- August 2011
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