抄録
<jats:p>In this paper <jats:italic>A</jats:italic> is a commutative noetherian ring, a an ideal of <jats:italic>A</jats:italic> and the <jats:italic>A</jats:italic>- modules are given the a-adic topology.</jats:p><jats:p>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.</jats:p>
収録刊行物
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- Mathematical Proceedings of the Cambridge Philosophical Society
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Mathematical Proceedings of the Cambridge Philosophical Society 108 (2), 231-246, 1990-09
Cambridge University Press (CUP)