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• W3136558626 abstract "Abstract We study direct-sum decompositions of torsion-free, finitely generated modules over a (commutative) Bass ring R through the factorization theory of the corresponding monoid T ( R ). Results of Levy–Wiegand and Levy–Odenthal together with a study of the local case yield an explicit description of T ( R ). The monoid is typically neither factorial nor cancellative. Nevertheless, we construct a transfer homomorphism to a monoid of graph agglomerations—a natural class of monoids serving as combinatorial models for the factorization theory of T ( R ). As a consequence, the monoid T ( R ) is transfer Krull of finite type and several finiteness results on arithmetical invariants apply. We also establish results on the elasticity of T ( R ) and characterize when T ( R ) is half-factorial. (Factoriality, that is, torsion-free Krull–Remak–Schmidt–Azumaya, is characterized by a theorem of Levy–Odenthal.) The monoids of graph agglomerations introduced here are also of independent interest." @default.
• W3136558626 created "2021-03-29" @default.
• W3136558626 creator A5069431545 @default.
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• W3136558626 date "2021-03-15" @default.
• W3136558626 modified "2023-09-25" @default.
• W3136558626 title "Lattices over Bass Rings and Graph Agglomerations" @default.
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• W3136558626 doi "https://doi.org/10.1007/s10468-021-10040-2" @default.
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