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Some homological properties of complete modules

Published online by Cambridge University Press:  24 October 2008

Anne-Marie Simon
Anne-Marie Simon
Affiliation:
Service d'algèbre C.P. 211, Université Libre de Bruxelles, Campus Plaine, Boulevard du Triomphe, B-1050 Bruxelles, Belgium
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Extract

In this paper A is a commutative noetherian ring, a an ideal of A and the A- modules are given the a-adic topology.

It is a general feeling that completeness is a kind of finiteness condition. We make precise that feeling and, after a result concerning the homology of a complex of complete modules which can be used in place of Nakayama's Lemma, we establish analogies between complete modules and finitely generated ones, with respect to flat dimension, injective dimension, Bass numbers and the Koszul complex. This is particularly clear in the local case, where we have also some partial information on the support of a complete module. With respect to dimension however, the analogy fails, as shown by an example.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 2 , September 1990 , pp. 231 - 246
Copyright
Copyright © Cambridge Philosophical Society 1990

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