Trace Ideals and the Gorenstein Property

2018/02/19 by Haydee Lindo, Lindo, Haydee, Nina Pande +1 · 3 citations
Mathematics · #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1802.06491

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.

Cited by

• Nearly Gorenstein blow-up algebras over two-dimensional regular local rings
• Characterization of almost Gorenstein rings in terms of the trace ideal
• Trace does not preserve Reflexivity

Related

• On the set of trace ideals of a Noetherian ring
• Rings whose ideals are isomorphic to trace ideals
• Correspondence between trace ideals and birational extensions with application to the analysis of the Gorenstein property of rings
• Annihilators of (co)homology and their influence on the trace Ideal
• Trace of canonical modules, annihilator of Ext, and classes of rings close to being Gorenstein