Leavitt path algebras which are Zorn rings

2013/02/19 by Rangaswamy, Kulumani M
#16D70 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1302.4681

Abstract

Let E be an arbitrary directed graph and let K be any field. It is shown that the Leavitt path algebra A of the graph E over the field K is a Zorn ring if and only if the graph E satisfies the Condition (L), that is, every cycle in E has an exit. It is also shown that the Leavitt path algebra A is a weakly regular ring if and only if every homomorphic image of A is a Zorn ring. The corresponding statement for graph C*-algebras is also investigated.

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