2026-05-31T13:36:25Zhttps://riuma.uma.es/rest/oai/request

oai:riuma.uma.es:10630/126262026-02-03T12:30:35Zcom_10630_2254col_10630_37959

Kanuni, Müge 2016-12-21T11:40:11Z 2016-12-21T11:40:11Z 2016-12-21 http://hdl.handle.net/10630/12626 A ring has invariant basis number property (IBN) if any two bases of a finitely generated free module have the same number of elements. In 1960's Leavitt constructed examples of rings R without IBN, more precisely for any positive integers m < n the ring R has a free module with a basis of m elements and another basis with n elements but no bases with k elements if k < n and not equal to m. Now, R is called a Leavitt algebra of type (m; n) and denoted by L(m; n). The Leavitt path algebras were defined just over a decade ago but they have roots in the works of Leavitt, as L(1; n) is algebra isomorphic to the Leavitt path algebra of the graph of a rose with n petals. Also, Cohn-Leavitt path algebras are a generalization of Leavitt path algebras which has both IBN and non-IBN examples. We will give the necessary and sufficient condition for a Cohn-Leavitt path algebra of a finite graph to have IBN. By using the non-stable K-theory, we provide Morita equivalent rings which are non-IBN, but are of different types. (This is joint work with M.Ozaydin). eng open access by-nc-nd Álgebra Leavitt path algebras and the IBN property conference output