t-Class semigroups of Noetherian domains

TL;DR

This paper explores the relationship between the ring-theoretic properties of Noetherian domains and the algebraic structure of their t-class semigroups, focusing on Clifford and Boolean properties.

Contribution

It provides a detailed analysis of how properties of Noetherian domains influence the structure of their t-class semigroups, especially regarding Clifford and Boolean characteristics.

Findings

Characterization of when the t-class semigroup is Clifford or Boolean

Connection between ring properties and semigroup structure

Conditions under which the t-class semigroup reflects domain properties

Abstract

The t-class semigroup of an integral domain is the semigroup of fractional t-ideals modulo its subsemigroup of nonzero principal ideals with the operation induced by ideal t-multiplication. This paper investigates ring-theoretic properties of a Noetherian domain that reflect reciprocally in the Clifford or Boolean property of its t-class semigroup.