On the equivalence of fsf and weakly Laskerian classes

TL;DR

This paper proves that over a Noetherian ring, the classes of weakly Laskerian and FSF modules are equivalent, and explores how this property behaves under certain ring extensions and tensor operations.

Contribution

It establishes the equivalence of weakly Laskerian and FSF modules over Noetherian rings and analyzes their behavior under ring extensions and tensoring.

Findings

Weakly Laskerian and FSF modules are the same over Noetherian rings.

The property of being weakly Laskerian descends via finite integral extensions.

The property ascends under tensoring with the completion.

Abstract

It is proved that, over a Noetherian ring R, the class of weakly Laskerian and FSF modules are the same classes. By using this characterization we proved that the property of being weakly Laskerian descends by finite integral extensions of local ring homomorphisms and ascends by tensoring under the completion.