English

On Gerko's Strongly Tor-independent Modules

Commutative Algebra 2020-12-08 v1

Abstract

Gerko proves that if an artinian local ring (R,mR)(R,\mathfrak{m}_R) possesses a sequence of strongly Tor-independent modules of length nn, then mRn0\mathfrak{m}_R^n\neq 0. This generalizes readily to Cohen-Macaulay rings. We present a version of this result for non-Cohen-Macaulay rings.

Keywords

Cite

@article{arxiv.2012.03361,
  title  = {On Gerko's Strongly Tor-independent Modules},
  author = {Hannah Altmann and Sean K. Sather-Wagstaff},
  journal= {arXiv preprint arXiv:2012.03361},
  year   = {2020}
}

Comments

8 pages

R2 v1 2026-06-23T20:45:58.668Z