Trace Ideals and the Gorenstein Property

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.

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)