Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2002-03

May 2002

Canonical Series for Bimodules and Modules

E. A. Whelan


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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