Prüfer modules over Leavitt path algebras

2017/07/12 by Gene Abrams, Abrams, Gene, Francesca Mantese +3
Mathematics · #16S99 (primary) #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16S99

paper · pdf · doi:10.48550/arxiv.1707.03732

24 pages. Submitted for publication July 2017. Comments are welcomed

arxiv created 2017/07/12 · arxiv updated 2017/07/13

Abstract

Let L_K(E) denote the Leavitt path algebra associated to the finite graph E and field K. For any closed path c in E, we define and investigate the uniserial, artinian, non-noetherian left L_K(E)-module U_E,c-1. The unique simple factor of each proper submodule of U_E,c-1 is isomorphic to the Chen simple module V_[c^∞]. In our main result, we classify those closed paths c for which U_E,c-1 is injective. In this situation, U_E,c-1 is the injective hull of V_[c^∞].

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