The Lipschitz Saturation of a Module

TL;DR

This paper extends the concept of Lipschitz saturation from ideals to modules, exploring different approaches and proving their generic equivalence, thereby advancing the theoretical understanding of module properties.

Contribution

It introduces new definitions of Lipschitz saturation for modules and demonstrates their generic equivalence, expanding the theoretical framework beyond ideals.

Findings

Different Lipschitz saturation definitions for modules are generically equivalent.

The work broadens the understanding of module saturation in Lipschitz geometry.

Abstract

In this work we extend the concept of the Lipschitz saturation of an ideal defined in [5] to the context of modules in some different ways, and we prove they are generically equivalent.