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# Radicalizers

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.## History

## Publication title

Communications in Algebra## Volume

45## Pagination

493-501## ISSN

0092-7872## Department/School

School of Natural Sciences## Publisher

Marcel Dekker Inc## Place of publication

270 Madison Ave, New York, USA, Ny, 10016## Rights statement

© 2017 Taylor & Francis## Repository Status

- Restricted