On the set of trace ideals of a Noetherian ring

TL;DR

This paper studies trace ideals in Noetherian rings, especially one-dimensional analytically irreducible local rings, and classifies Gorenstein rings with finitely many trace ideals.

Contribution

It provides a classification of Gorenstein rings with a finite set of trace ideals within a specific class of Noetherian rings.

Findings

Gorenstein rings with finitely many trace ideals are characterized.

Classification results for trace ideals in one-dimensional analytically irreducible local rings.

Insights into the structure of trace ideals in Noetherian rings.

Abstract

We consider trace ideals in Noetherian rings and focus our attention to one-dimensional analytically irreducible local rings. For such rings we classify those Gorenstein rings which admit only a finite number of trace ideals.