Cohn Path Algebras have Invariant Basis Number

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, and the Invariant Matrix Number property.

Key Words:

• Cohn path algebra
• Invariant Basis Number
• Leavitt path algebra

2010 Mathematics Subject Classification:

• Primary: 16S99
• Secondary: 05C25

ACKNOWLEDGMENT

We thank T. Dorsey for suggesting a streamlined version of Proposition 8. We also thank the referee for his/her very thorough referee report, which included the observation made subsequent to Example 12, as well as a suggestion regarding a clarification of the proof of Theorem 9.

M. Kanuni would like to thank the whole UCCS Math Department for their hospitality during her visit when this article was written.

Notes

Communicated by T. Albu.