Largest ideals in Leavitt path algebras

2019/05/24 by Cam, Vural, Canto, Cristóbal Gil, Kanuni, Müge +1
#16D25 #16D30 (Secondary) #16D70 (Primary) #16E20 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1905.10160

Abstract

We identify largest ideals in Leavitt path algebras: the largest locally left/right artinian (which is the largest semisimple one), the largest locally left/right noetherian without minimal idempotents, the largest exchange, and the largest purely infinite. This last ideal is described as a direct sum of purely infinite simple pieces plus purely infinite non-simple and non-decomposable pieces. The invariance under ring isomorphisms of these ideals is also studied.

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