Entropy on modules over the group ring of a sofic group

TL;DR

This paper extends Peters' entropy formula to modules over group rings of sofic groups and explores the connection between entropy values and the zero divisor conjecture.

Contribution

It generalizes Peters' formula to modules over group rings of sofic groups and investigates the relationship between entropy and the zero divisor conjecture.

Findings

Partial generalization of Peters' entropy formula

Discussion on entropy values and the zero divisor conjecture

Insights into modules over group rings of sofic groups

Abstract

We partially generalize Peters' formula on modules over the group ring ${\mathbb F} \Gamma$ for a given finite field ${\mathbb F}$ and a sofic group $\Gamma$. It is also discussed that how the values of entropy are related to the zero divisor conjecture.