Homological flat dimensions

Details Homological flat dimensions Homological flat dimensions

2007-09-26

arxiv.org/abs/0709.4078v2

Mathematics

Commutative Algebra

24pages

Scientific paper

For finitely generated module $M$ over a local ring $R$, the conventional notions of complete intersection dimension $\cid_R M$ and Cohen-Macaulay dimension $\cmdim_R M$ do not extend to cover the case of infinitely generated modules. In this paper we introduce similar invariants for not necessarily finitely generated modules, (namely, complete intersection flat and Cohen-Macaulay flat dimensions) which for finitely generated modules, coincide with the corresponding classical ones.

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