Cohn-Leavitt Path Algebras and the Invariant Basis Number Property

We give the necessary and sufficient condition for a separated Cohn-Leavitt path algebra of a finite digraph to have IBN. As a consequence, separated Cohn path algebras have IBN. We determine the non-stable K-theory of a corner ring in terms of the non-stable K-theory of the ambient ring. We give a...

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Bibliographic Details
Published in:arXiv.org 2016-06
Main Authors: Kanuni, Müge, Özaydın, Murad
Format: Article
Language:English
Subjects:
Algebra
Graph theory
Online Access:Get full text
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Summary:We give the necessary and sufficient condition for a separated Cohn-Leavitt path algebra of a finite digraph to have IBN. As a consequence, separated Cohn path algebras have IBN. We determine the non-stable K-theory of a corner ring in terms of the non-stable K-theory of the ambient ring. We give a necessary condition for a corner algebra of a separated Cohn-Leavitt path algebra of a finite graph to have IBN. We provide Morita equivalent rings which are non-IBN, but are of different types.
ISSN:2331-8422
DOI:10.48550/arxiv.1606.07998