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The singular ideal and radicals

Part of: Modules, bimodules and ideals Radicals and radical properties of rings

Published online by Cambridge University Press:  09 April 2009

Miguel Ferrero  and
Edmund R. Puczyłowski
Miguel Ferrero
Affiliation:
Instituto de Matemática Universidade Federal do Rio Grande do Sul91509-900 Porto AlegreBrazil email: [email protected]
Edmund R. Puczyłowski
Affiliation:
Institute of Mathematics University of Warsaw02-097 Warsaw, Banacha 2Poland email: [email protected]
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Abstract

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Some properties of the singular ideal are established. In particular its behaviour when passing to one-sided ideals is studied. Obtained results are applied to study some radicals related to the singular ideal. In particular a radical S such that for every ring R, S(R) and R/S(R) are close to being a singular ring and a non-singular ring, respectively, is constructed.

Keywords

singular idealradical classes.

MSC classification

Secondary: 16D80: Other classes of modules and ideals 16N60: Prime and semiprime rings 16N80: General radicals and rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 64 , Issue 2 , April 1998 , pp. 195 - 209
Copyright
Copyright © Australian Mathematical Society 1998

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