On Monoid Algebras Having Every Nonempty Subset of $${\mathbb {N}}_{\ge 2}$$ as a Length Set
Abstract We construct monoid algebras that satisfy the ascending chain condition on principal ideals and have the property that every nonempty subset of $$\mathbb N_{\ge 2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mrow> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:math> occurs as a length set.
Authors
- Alfred Geroldinger (ORCID: https://orcid.org/0000-0003-0026-2273)
- Felix Gotti (ORCID: https://orcid.org/0000-0002-5313-2141)
Institutions
- University of Graz (AT)
- Massachusetts Institute of Technology (US)
Publication Details
- Journal
- Mediterranean Journal of Mathematics
- Published
- 2025-04-12
- DOI
- https://doi.org/10.1007/s00009-025-02835-0
- Citations
- 1
- Primary Topic
- Rings, Modules, and Algebras
- Type
- article
- Field-Weighted Citation Impact
- 5.38
Funders
- National Science Foundation
- Massachusetts Institute of Technology
- Austrian Science Fund