# On the Noether Bound for Noncommutative Rings

## TL;DR

This paper constructs two noncommutative algebras with cyclic group actions demonstrating that generators of degree 3n are necessary, highlighting limitations in the Noether bound for such rings.

## Contribution

It introduces explicit examples of noncommutative algebras with cyclic group actions that require high-degree generators, advancing understanding of the Noether bound in noncommutative settings.

## Key findings

- Two explicit noncommutative algebras with cyclic group actions
- Generators of degree 3n are necessary for these algebras
- Results show limitations of the Noether bound in noncommutative rings

## Abstract

We present two noncommutative algebras over a field of characteristic zero that each posses a family of actions by cyclic groups of order $2n$, represented in $n \times n$ matrices, requiring generators of degree $3n$.