A criterion for Leavitt path algebras having invariant basis number

Abstract

In this paper, we give a matrix-theoretic criterion for the Leavitt path algebra of a finite graph has Invariant Basis Number. Consequently, we show that the Cohn path algebra of a finite graph has Invariant Basis Number, as well as provide some certain classes of finite graphs for which Leavitt path algebras having Invariant Basis Number.

21 pages. arXiv admin note: substantial text overlap with arXiv:1603.09695