English

Cohen Factorizations: Weak Functoriality and Applications

Commutative Algebra 2013-06-03 v3

Abstract

We investigate Cohen factorizations of local ring homomorphisms from three perspectives. First, we prove a "weak functoriality" result for Cohen factorizations: certain morphisms of local ring homomorphisms induce morphisms of Cohen factorizations. Second, we use Cohen factorizations to study the properties of local ring homomorphisms (Gorenstein, Cohen-Macaulay, etc.) in certain commutative diagrams. Third, we use Cohen factorizations to investigate the structure of quasi-deformations of local rings, with an eye on the question of the behavior of CI-dimension in short exact sequences.

Keywords

Cite

@article{arxiv.1205.2119,
  title  = {Cohen Factorizations: Weak Functoriality and Applications},
  author = {Saeed Nasseh and Sean Sather-Wagstaff},
  journal= {arXiv preprint arXiv:1205.2119},
  year   = {2013}
}

Comments

25 pages, uses xypic. In V.2, statement of Theorem C is modified, Example 3.5 is new, and Remarks 4.10 and 5.3 are new. v.3 only small editorial changes to 4.10 and acknowledgements. Final version to appear in JPAA

R2 v1 2026-06-21T21:01:10.737Z