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Quasivarieties of Modules Over Path Algebras of Quivers

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Abstract

Let FΛ be a finite dimensional path algebra of a quiver Λ over a field F. Let L and R denote the varieties of all left and right FΛ-modules respectively. We prove the equivalence of the following statements.

  • The subvariety lattice of L is a sublattice of the subquasivariety lattice of L.

  • The subquasivariety lattice of R is distributive.

  • Λ is an ordered forest.

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Authors and Affiliations

  1. Department of Mathematics, University of Colorado, Boulder, 80309-0395, CO, USA

    Keith A. Kearnes

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  1. Keith A. Kearnes
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Correspondence to Keith A. Kearnes.

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Dedicated to the memory of Willem Johannes Blok

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Kearnes, K.A. Quasivarieties of Modules Over Path Algebras of Quivers. Stud Logica 83, 333–349 (2006). https://doi.org/10.1007/s11225-006-8307-3

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  • DOI: https://doi.org/10.1007/s11225-006-8307-3

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