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Mathematics > Commutative Algebra

arXiv:1805.02911 (math)
[Submitted on 8 May 2018]

Title:Sets of Arithmetical Invariants in Transfer Krull Monoids

Authors:Alfred Geroldinger, Qinghai Zhong
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Abstract:Transfer Krull monoids are a recent concept including all commutative Krull domains and also, for example, wide classes of non-commutative Dedekind domains. We show that transfer Krull monoids are fully elastic (i.e., every rational number between $1$ and the elasticity of the monoid can be realized as the elasticity of an element). In commutative Krull monoids which have sufficiently many prime divisors in all classes of their class group, the set of catenary degrees and the set of tame degrees are intervals. Without the assumption on the distribution of prime divisors, arbitrary finite sets can be realized as sets of catenary degrees and as sets of tame degrees.
Subjects: Commutative Algebra (math.AC); Combinatorics (math.CO); Group Theory (math.GR)
MSC classes: 20M13, 13A05, 13F05, 16H10, 16U30
Cite as: arXiv:1805.02911 [math.AC]
  (or arXiv:1805.02911v1 [math.AC] for this version)
  https://doi.org/10.48550/arXiv.1805.02911
Journal reference: J. Pure Appl. Algebra,2019
Related DOI: https://doi.org/10.1016/j.jpaa.2018.12.011

Submission history

From: Qinghai Zhong [view email]
[v1] Tue, 8 May 2018 09:18:53 UTC (30 KB)
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