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.
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The subvariety lattice of L is a sublattice of the subquasivariety lattice of L.
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The subquasivariety lattice of R is distributive.
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Λ is an ordered forest.
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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