论文标题
低音环和图形团聚的晶格
Lattices over Bass rings and graph agglomerations
论文作者
论文摘要
我们通过相应的单体$ t（r）$的分解理论研究了无扭转的，有限生成的模块的直接和分解。 Levy-Wiegand和Levy-Eodenthal的结果以及对当地案件的研究产生了$ t（r）$的明确描述。单体通常既不是阶乘也不是取消的。然而，我们将传输同态构建到一个图形团聚的单体 - 一种天然类的单体类别，是$ t（r）$的分解理论的组合模型。结果，Monoid $ t（R）$是有限类型的转移Krull，并且适用算术不变的几个有限结果。我们还建立了$ t（r）$的弹性的结果，并在$ t（r）$是一半时特征。 （阶乘，即无扭转的krull-remak-schmidt-azumaya，其特征是levy-odtheral的定理。）此处介绍的图形集聚的单体也具有独立的兴趣。
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.
