The addition on totally positive integers uniquely determines the totally real number field
Year: 2026
Type: preprint
Abstract: Let $K$ be a totally real number field. We prove that the totally positive algebraic integers $\mathcal O_K^+$ of $K$, viewed as an abstract additive semigroup, uniquely determine $K$. We also describe all the additive relations by giving a presentation of $\mathcal O_K^+$ in terms of indecomposables as generators and a certain concrete set of generating relations. In fact, we obtain this presentation in a more general class of discrete semigroups which we call semilattices.
Source: arXiv (Cornell University)
Authors: Kala, Vitezslav, Roy, Ritoprovo
Institution: Charles University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: European Commission
Awards: G3810236772, G4396925471
OpenAlex ID: W7212124692