English

Trace Ideals and the Gorenstein Property

Commutative Algebra 2018-04-10 v2

Abstract

Let R be a local Noetherian commutative ring. We prove that R is an Artinian Gorenstein ring if and only if every ideal in R is a trace ideal. We discuss when the trace ideal of a module coincides with its double annihilator.

Keywords

Cite

@article{arxiv.1802.06491,
  title  = {Trace Ideals and the Gorenstein Property},
  author = {Haydee Lindo and Nina Pande},
  journal= {arXiv preprint arXiv:1802.06491},
  year   = {2018}
}

Comments

6 pages. Comments welcome In version 2, the main results are the same. Changes: 1) Addition of Reference: Ding [4] 2) New Lemma: Lemma 2.8 3) Correction/Change in statement and proof of Cor 2.9 (prev Cor 2.8) 4) Some cosmetic edits (e.g diagram in Remark 3.2)

R2 v1 2026-06-23T00:26:00.515Z