We study one-dimensional Cohen-Macaulay rings whose trace ideal of the canonical
module is as small as possible. In this paper we call such rings far-flung Gorenstein rings …

This article investigates the traces of certain modules over rings of invariants associated with
finite groups. More precisely, we provide a formula for computing the traces of arbitrary semi …

We prove a tight connection between reflexive modules over a one-dimensional ring $ R $
and its birational extensions that are self-dual as $ R $-modules. Consequently, we show …

We investigate a problem of when commutative local domains have a finite number of trace
ideals. The problem is left for the case of dimension one. In this paper, with a necessary …

In this paper, we study Noetherian local rings R having a finite number of trace ideals. We
proved that such rings are of dimension at most two. Furthermore, if the integral closure of …

This study investigates the structure of Arf rings. From the perspective of ring extensions, a
decomposition of integrally closed ideals is given. Using this, we present a kind of their …

In the present paper we investigate reflexive modules over the endomorphism algebras of
reflexive trace ideals in a one-dimensional Cohen-Macaulay local ring. The main theorem …

Motivated by some recent results of F. P\'erez and RRG connecting test ideal of module
closure operations and trace ideals, we investigate the test ideal restricted to principal ideals …

On Reflexive Ideals Page 1 On Reflexive Ideals Pietro Campochiaro Scuola Superiore di
Catania from a joint work in progress with M. D’Anna and F. Strazzanti 08 July 2024 Page 2 …