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Normalising elements and radicals, I.

Published online by Cambridge University Press:  17 April 2009

E.A. Whelan
E.A. Whelan
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich, Norfolk NR4 7TJ, England.
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Abstract

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In this paper we study rings and bimodules with no known one-sided chain conditions, but whose (two-sided) ideals and subbimodules are ‘nicely’ generated. We define bi-noetherian polycentral (BPC) and bi-noetherian polynormal (BPN) rings and bimodules, large classes of (almost always) non-noetherian objects, and put on record the basic facts about them. Any BPC ring is a BPN ring. In the case of rings we reduce their properties to properties of the prime ideals, and study the d.c.c. on (two-sided) ideals. We define both the artinian and bi-artinian radicals of a BPN ring, and use them to show that for BPN rings the intersections of the powers of both the Brown-McCoy and the Jacobson radicals are zero.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 1 , February 1989 , pp. 81 - 106
Copyright
Copyright © Australian Mathematical Society 1989

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