On Partial Trace Ideals

TL;DR

This paper explores the properties of partial trace ideals, providing new theoretical insights, bounds, and explicit formulas, especially for numerical semigroup rings generated by three elements.

Contribution

It establishes key properties of partial trace ideals, answers open questions, and derives explicit formulas for specific cases, advancing understanding in this area.

Findings

Partial trace ideals have specific properties confirmed.

An upper bound for an invariant related to the canonical module is established.

Explicit formulas are derived for numerical semigroup rings generated by three elements.

Abstract

We investigate the notion of partial trace ideals, recently introduced by Maitra. We first establish several properties of partial trace ideals and give affirmative answers to questions posed by Maitra. We then study the invariant defined by the partial trace ideal of the canonical module, and obtain an upper bound that recovers one direction of a result of Kobayashi. Moreover, in the case of numerical semigroup rings generated by three elements, we provide an explicit formula for this invariant.