Cohn path algebras have Invariant Basis Number

TL;DR

This paper proves that Cohn path algebras associated with finite directed graphs over any field possess the Invariant Basis Number property, ensuring consistent module rank comparisons.

Contribution

It establishes that all Cohn path algebras of finite graphs over any field have the Invariant Basis Number property, a new result in algebraic structure theory.

Findings

Cohn path algebras have the Invariant Basis Number property

The result holds for all finite graphs and any field

Provides a foundational property for module theory over these algebras

Abstract

For any finite directed graph $E$ and any field $K$ we show that the Cohn path algebra $C_K(E)$ has the Invariant Basis Number property.