# Zero divisors and units with small supports in group algebras of torsion-free groups

## TL;DR

This paper introduces a graph-based approach to study zero divisors and units with small supports in group algebras of torsion-free groups, providing new insights into their algebraic structure.

## Contribution

It develops a novel graph-theoretic framework to analyze zero divisors and units in group algebras of torsion-free groups, advancing understanding of their properties.

## Key findings

- Graph association reveals structural constraints on zero divisors.
- Identifies conditions under which small support units can exist.
- Provides tools for further algebraic investigations in torsion-free group algebras.

## Abstract

We associate a graph to a possible non-zero zero-divisor in the group algebra of a torsion-free group.