# A commutative noetherian local ring of embedding dimension 4 having a transcendental series of Betti numbers

## TL;DR

This paper constructs specific examples of commutative noetherian local rings of embedding dimension 4 that exhibit transcendental Betti number series, revealing complex algebraic behaviors.

## Contribution

It introduces new examples of local rings with exotic properties, utilizing computational tools and building on prior theoretical results.

## Key findings

- Constructed a local ring with transcendental Betti series.
- Developed methods combining Macaulay2 and theoretical insights.
- Produced additional rings with unusual algebraic properties.

## Abstract

We construct a ring with the properties of the title of the paper. We also construct some other local rings of embedding dimension 4 with exotic properties. Among the methods used are the {\tt Macaulay2}-package {\tt DGAlgebras} by Frank Moore, combined with and inspired by results by Anick, Avramov, Backelin, Katth\"an, Lemaire, Levin, L\"ofwall and others.