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.
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)