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<p>We study algebraic and arithmetic properties of submonoids (resp. subrings) of factorial monoids (resp. factorial domains) whose non-invertible elements all lie in the conductor. This continues earlier work of Baeth, Cisto, et al. On our way we answer several conjectures, formulated in their papers in the affirmative ( [<CitationRef CitationID="CR1">1</CitationRef>, Conjecture 4.16] and [<CitationRef CitationID="CR6">6</CitationRef>, Conjectures 7 and 13, and Section 9]).</p>

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On conductor submonoids of factorial monoids

  • 期刊论文

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  • 发表日期：

    2025年9月30日

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  • Alfred Geroldinger,
  • Weihao Yan,
  • Qinghai Zhong

摘要

We study algebraic and arithmetic properties of submonoids (resp. subrings) of factorial monoids (resp. factorial domains) whose non-invertible elements all lie in the conductor. This continues earlier work of Baeth, Cisto, et al. On our way we answer several conjectures, formulated in their papers in the affirmative ( [1, Conjecture 4.16] and [6, Conjectures 7 and 13, and Section 9]).