Quasivarieties of Modules Over Path Algebras of Quivers

Studia Logica 83 (1-3):333-349 (2006)
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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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