# Inverse limits of Macaulay's inverse systems

## TL;DR

This paper generalizes existing results on inverse limits of Macaulay's inverse systems for Cohen-Macaulay algebras, introduces a strictness result for filtrations, and extends several classical lemmas and isomorphisms.

## Contribution

It provides a new description of inverse limits of Macaulay's inverse systems for Cohen-Macaulay factor algebras, extending previous work and unifying several key algebraic results.

## Key findings

- Describes inverse limits of Macaulay's inverse systems for Cohen-Macaulay algebras
- Establishes a strictness result for filtrations defined by regular sequences
- Generalizes a lemma of Uli Walther and the Rees isomorphism

## Abstract

Generalizing a result of Masuti and the second author, we describe inverse limits of Macaulay's inverse systems for Cohen-Macaulay factor algebras of formal power series or polynomial rings over an infinite field. On the way we find a strictness result for filtrations defined by regular sequences. It generalizes both a lemma of Uli Walther and the Rees isomorphism.