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On monoid algebras having every nonempty subset of $\mathbb{N}_{\ge 2}$ as a length set

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arxiv 2404.11494 v1 pith:R2SY5RYG submitted 2024-04-17 math.AC

Alfred Geroldinger , Felix Gotti This is my paper · ORCID
classification math.AC
keywords algebraseverylengthmathbbmonoidnonemptysubsetascending
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abstract

We construct monoid algebras which satisfy the ascending chain condition on principal ideals and which have the property that every nonempty subset of $\mathbb{N}_{\ge 2}$ occurs as a length set.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties

    math.RA 2025-02 accept novelty 7.0 of 10

    The category of atomic monoids with atom-preserving homomorphisms is complete and cocomplete, with explicit product, coproduct, equalizer, and pullback constructions and length-set formulas.

  2. On the ascent of almost and quasi-atomicity to monoid semidomains

    math.AC 2025-01 conditional novelty 6.0 of 10

    Quasi-atomicity does not ascend to polynomial extensions in general, and neither almost nor quasi-atomicity ascend to monoid domains over finite fields.

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