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  • Lattices over Bass rings and graph agglomerations
    Baeth, Nicholas R. ; Smertnig, Daniel
    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.
    Source: Algebras and representation theory. - ISSN 1386-923X (Vol. 25, iss. 3, Jun. 2022, str. 669-704)
    Type of material - article, component part ; adult, serious
    Publish date - 2022
    Language - english
    COBISS.SI-ID - 172426499

    Link(s):

    https://link.springer.com/article/10.1007/s10468-021-10040-2
    DOI

source: Algebras and representation theory. - ISSN 1386-923X (Vol. 25, iss. 3, Jun. 2022, str. 669-704)
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