<p>We construct monoid algebras that satisfy the ascending chain condition on principal ideals and have the property that every nonempty subset of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2835_Article_IEq3.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb N_{\ge 2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">N</mi> <mrow> <mo>≥</mo> <mn>2</mn> </mrow> </msub> </math></EquationSource> </InlineEquation> occurs as a length set.</p>

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On Monoid Algebras Having Every Nonempty Subset of \({\mathbb {N}}_{\ge 2}\) as a Length Set

  • Alfred Geroldinger,
  • Felix Gotti

摘要

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