Homological flat dimensions

Parviz Sahandi; Tirdad Sharif; Siamak Yassemi

Homological flat dimensions

Commutative Algebra 2008-02-04 v2

Authors: Parviz Sahandi , Tirdad Sharif , Siamak Yassemi

Abstract

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.

Keywords

cohen-macaulay rings and modules commutative algebra module theory

Cite

@article{arxiv.0709.4078,
  title  = {Homological flat dimensions},
  author = {Parviz Sahandi and Tirdad Sharif and Siamak Yassemi},
  journal= {arXiv preprint arXiv:0709.4078},
  year   = {2008}
}

Comments

24pages

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