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PreprintarXiv licencearXiv

The addition on totally positive integers uniquely determines the totally real number field

  • Vitezslav Kala
  • Ritoprovo Roy
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Abstract

Let K be a totally real number field. We prove that the totally positive algebraic integers 𝒪K+ of K, viewed as an abstract additive semigroup, uniquely determine K. We also describe all the additive relations by giving a presentation of 𝒪K+ 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.

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Cite

BibTeXRIS
BibTeX
@misc{kala2026addition,
  title = {{The addition on totally positive integers uniquely determines the totally real number field}},
  author = {Vitezslav Kala and Ritoprovo Roy},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09346},
  eprint = {2609.09346},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09346},
}
RIS
TY  - UNPB
TI  - The addition on totally positive integers uniquely determines the totally real number field
AU  - Vitezslav Kala
AU  - Ritoprovo Roy
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09346
UR  - https://arxiv.org/abs/2609.09346
AB  - Let K be a totally real number field. We prove that the totally positive algebraic integers 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 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.
ER  -