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ACCESSIBLE SUBRINGS AND KUROSH’S CHAINS OF ASSOCIATIVE RINGS

Part of: Modules, bimodules and ideals Rings and algebras arising under various constructions

Published online by Cambridge University Press:  18 July 2013

RYSZARD R. ANDRUSZKIEWICZ  and
MAGDALENA SOBOLEWSKA
RYSZARD R. ANDRUSZKIEWICZ*
Affiliation:
Institute of Mathematics, University of Białystok, 15-267 Białystok, Akademicka 2, Poland email [email protected]
MAGDALENA SOBOLEWSKA
Affiliation:
Institute of Mathematics, University of Białystok, 15-267 Białystok, Akademicka 2, Poland email [email protected]
*
✉[email protected]
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Abstract

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This article is devoted to the historical study of the ADS-problem with a special emphasis on the use of methods and techniques, emerging with the development of the theory of rings: accessible subrings, iterated maximal essential extensions of rings, completely normal rings. We construct new examples of classes for which Kurosh’s chain stabilizes at any given step. We recall the old nontrivial questions, and we pose a new one.

Keywords

stabilization of Kurosh’s chainsconstruction of classesaccessible subringsiterated maximal essential extensions of ringscompletely normal rings

MSC classification

Secondary: 16D25: Ideals 16S70: Extensions of rings by ideals
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 95 , Issue 2 , October 2013 , pp. 145 - 157
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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