# Mixed multiplicities and the multiplicity of rees modules of reductions (published in j. Algebra appl.)

## TL;DR

This paper establishes that mixed multiplicities and the multiplicity of Rees modules are equal for good filtrations and their reductions, leading to new insights in algebraic multiplicity theory.

## Contribution

It proves the equality of mixed multiplicities and Rees module multiplicities for good filtrations and their reductions, a novel result in algebraic multiplicity theory.

## Key findings

- Mixed multiplicities equal the multiplicity of Rees modules for good filtrations.
- Results apply to reductions of filtrations, simplifying multiplicity calculations.
- Provides new theorems on the structure of Rees modules and their multiplicities.

## Abstract

This paper shows that mixed multiplicities and the multiplicity of Rees modules of good filtrations and that of their reductions are the same. As an application of this result, we obtain interesting results on mixed multiplicities and the multiplicity of Rees modules.