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Openness of various loci over Noetherian rings

Commutative Algebra 2022-01-31 v1

Abstract

In this paper, we consider the openness of the P-locus of a finitely generated module over a commutative noetherian ring in the case where P is each of the properties FID, Gor, CM, MCM, (S_n), and (T_n). One of the main results asserts that FID-loci over an acceptable ring are open. We give a module version of the Nagata criterion, and prove that it holds for all of the aforementioned properties.

Keywords

Cite

@article{arxiv.2201.11955,
  title  = {Openness of various loci over Noetherian rings},
  author = {Kaito Kimura},
  journal= {arXiv preprint arXiv:2201.11955},
  year   = {2022}
}

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13 pages