Radicalizers |
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Authors: | B J Gardner |
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Institution: | 1. Discipline of Mathematics, University of Tasmania, Hobart, Tasmania, AustraliaBarry.Gardner@utas.edu.au |
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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. |
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Keywords: | Idealizer metaideal radical class |
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