Star-Invertibility and $t$-finite character in Integral Domains

TL;DR

This paper explores conditions on integral ideals in integral domains to determine when the domain has $t$-finite character and examines issues related to the local invertibility of these ideals.

Contribution

It introduces new conditions on families of ideals to characterize $t$-finite character and investigates local invertibility problems in integral domains.

Findings

Established criteria for $t$-finite character in integral domains.

Analyzed the relationship between ideal invertibility and domain properties.

Provided new insights into the structure of integral ideals in relation to $t$-maximal ideals.

Abstract

Let $A$ be an integral domain. We study new conditions on families of integral ideals of $A$ in order to get that $A$ is of $t$-finite character (i.e., each nonzero element of $A$ is contained in finitely many $t$-maximal ideals). We also investigate problems connected with the local invertibility of ideals.