Integral domains with Boolean t-Class semigroup

TL;DR

This paper studies integral domains where the t-class semigroup is Boolean, focusing on GCD and stability conditions, and extends known results from Prufer and Bezout domains of finite character.

Contribution

It introduces t-analogues of classical results for Prufer and Bezout domains, deepening understanding of Boolean t-class semigroups in integral domains.

Findings

Characterization of integral domains with Boolean t-class semigroup

Extension of classical results to t-analogues in Prufer and Bezout domains

Insights into GCD and stability conditions in these domains

Abstract

The t-class semigroup of an integral domain is the semigroup of the isomorphy classes of the t-ideals with the operation induced by t-multiplication. This paper investigates integral domains with Boolean t-class semigroup with an emphasis on the GCD and stability conditions. The main results establish t-analogues for well-known results on Prufer domains and Bezout domains of finite character.