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ON $\alpha $-LIKE RADICALS OF RINGS

Part of: Radicals and radical properties of rings

Published online by Cambridge University Press:  12 December 2012

H. FRANCE-JACKSON ,
T. KHULAN  and
S. TUMURBAT
H. FRANCE-JACKSON*
Affiliation:
Department of Mathematics and Applied Mathematics, Summerstrand Campus (South), PO Box 77000, Nelson Mandela Metropolitan University, Port Elizabeth 6031, South Africa
T. KHULAN
Affiliation:
Department of Algebra, University of Mongolia, PO Box 75, Ulaan Baatar 20, Mongolia email [email protected]
S. TUMURBAT
Affiliation:
Department of Algebra, University of Mongolia, PO Box 75, Ulaan Baatar 20, Mongolia email [email protected]
*
✉[email protected]
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Abstract

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Let $\alpha $ be any radical of associative rings. A radical $\gamma $ is called $\alpha $-like if, for every $\alpha $-semisimple ring $A$, the polynomial ring $A[x] $ is $\gamma $-semisimple. In this paper we describe properties of $\alpha $-like radicals and show how they can be used to solve some open problems in radical theory.

Keywords

prime-like radicalα-like radicalspecial radicalAmitsur property of radicalspolynomially extensible radicals

MSC classification

Secondary: 16N80: General radicals and rings
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 2 , October 2013 , pp. 331 - 339
Copyright
Copyright ©2012 Australian Mathematical Publishing Association Inc. 

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