THE AUSLANDER-REITEN QUIVERS OF NONLOCAL BASS RINGS

In this paper, we analyze the Auslander-Reiten quiver for the category of lattices over a commutative, non-local, Bass ring. Our applications include explicitly describing the quiver, proving path connectedness and Eulerian features of the quiver, associating the quiver to a Cayley diagram, proving a finite type result with the quiver and generalizing the concept of unique factorization domain to the notion of unique map factorization domain.1