Smooth sequences and overring operators

TL;DR

This paper introduces smooth sequences of integral domains and overring operators, providing new conditions for kernel freeness in extension maps between groups of invertible ideals of Pr"ufer domains.

Contribution

It presents a novel framework of smooth sequences and overring operators to analyze kernel freeness in Pr"ufer domain extensions.

Findings

Conditions for kernel freeness in extension maps

Construction of smooth sequences via overring operators

Application to groups of invertible ideals

Abstract

We introduce smooth sequences of integral domains as well-ordered ascending chains that behave well at limit ordinals. Subsequently, we use this notion to give some conditions on the freeness of kernels of extension maps between groups of invertible ideals of Pr\"ufer domains. We also define overring operators to construct smooth sequences in a recursive way.