Centre for Discrete and Applicable Mathematics

CDAM Research Report, LSE-CDAM-2002-03

May 2002

Canonical Series for Bimodules and Modules

E. A. Whelan

Abstract

We establish the existence of unique lower canonical (ascending) and upper canonical (descending) sequences of sub-bimodules for many bimodules $_\Delta B _\Lambda$ over unital rings $\Delta$ , $\Lambda$ , including all cases in which $\Lambda$ satisfies the ascending chain condition on two-sided ideals. Our methods work not only for rings, but also when $\Delta$ and $\Lambda$ are ``(associative) rings not necessarily with unity'', provided that $\Lambda$ is fully finitely separated. This property, which is inherited by two-sided ideals of any such $\Lambda$ , is also studied.

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		CDAM Research Reports Series Centre for Discrete and Applicable Mathematics London School of Economics Houghton Street London WC2A 2AE, U.K.
		Phone: +44(0)-20-7955 7732. Fax: +44(0)-20-7955 6877. Email: info@maths.lse.ac.uk