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Abstract

For a Kurosh–Amitsur radical class of rings, we investigate the existence, for a radical subring S of a ring A, of a largest subring T of A for which S is the radical. When T exists, it is called the radicalizer of S. There are no radical classes of associative rings for which every radical subring of every ring has a radicalizer. If a subring is the radical of its idealizer, then the idealizer is a radicalizer. We examine radical classes for which each radical subring is contained in one which is the radical of its own idealizer.

Item Type:	Article
Authors/Creators:	Gardner, BJ
Keywords:	ring, radical, idealizer, metaideal
Journal or Publication Title:	Communications in Algebra
Publisher:	Marcel Dekker Inc
ISSN:	0092-7872
DOI / ID Number:	10.1080/00927872.2016.1175467
Copyright Information:	© 2017 Taylor & Francis
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