Lattices over Bass Rings and Graph Agglomerations

Abstract We study direct-sum decompositions of torsion-free, finitely generated modules over a (commutative) Bass ring R through the factorization theory corresponding monoid T ( ). Results Levy–Wiegand and Levy–Odenthal together with local case yield an explicit description The is typically neither factorial nor cancellative. Nevertheless, we construct transfer homomorphism to graph agglomerations—a natural class monoids serving as combinatorial models for As consequence, ) Krull finite type several finiteness results on arithmetical invariants apply. also establish elasticity characterize when half-factorial. (Factoriality, that is, torsion-free Krull–Remak–Schmidt–Azumaya, characterized by theorem Levy–Odenthal.) agglomerations introduced here are independent interest.