The generic equivalence among the Lipschitz saturation of a sheaf of modules

TL;DR

This paper extends the concept of Lipschitz saturation from ideals to modules and demonstrates their generic equivalence, broadening the understanding of module saturation in mathematical analysis.

Contribution

It introduces new definitions of Lipschitz saturation for modules and proves their generic equivalence, advancing the theory of module saturation.

Findings

Lipschitz saturation concepts for modules are introduced.

The different notions of saturation are shown to be generically equivalent.

The work broadens the theoretical framework of module saturation.

Abstract

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