Embedding group algebras into finite von Neumann regular rings

TL;DR

This paper proves that group algebras over fields of characteristic zero can be embedded into von Neumann regular rings, providing insights related to the Atiyah conjecture.

Contribution

It introduces a method to embed group algebras into von Neumann regular rings, advancing understanding of algebraic structures and their relation to the Atiyah conjecture.

Findings

KG can be embedded into a von Neumann unit-regular ring

Results obtained have implications for the Atiyah conjecture

Provides a new approach to studying group algebras and regular rings

Abstract

Let G be a group and let K be a field of characteristic zero. We shall prove that KG can be embedded into a von Neumann unit-regular ring. In the course of the proof, we shall obtain a result relevant to the Atiyah conjecture.