On Waring numbers of henselian rings
Abstract Let be a positive integer. Let be a henselian local ring with residue field of th level . We give some upper and lower bounds for the th Waring number in terms of and . In large number of cases, we are able to compute . Similar results for the th Waring number of the total ring of fractions of are obtained. We then provide applications. In particular, we compute and for and any prime .
Authors
- Piotr Miska (ORCID: https://orcid.org/0000-0002-6792-8634)
- Tomasz Kowalczyk (ORCID: https://orcid.org/0000-0002-5220-043X)
Institutions
- Jagiellonian University (PL)
- Institute of Mathematics (PL)
Publication Details
- Journal
- Mathematika
- Published
- 2024-08-25
- DOI
- https://doi.org/10.1112/mtk.12276
- Citations
- 2
- Primary Topic
- Rings, Modules, and Algebras
- Type
- article
- Field-Weighted Citation Impact
- 1.27
Funders
- Narodowe Centrum Nauki