Power-integral matrices over number fields: the Drazin inverse, pseudo-determinant, and numerical semigroups

Theo Chinn; Junshu Feng; Stephan Ramon Garcia; Hechun Zhang

Power-integral matrices over number fields: the Drazin inverse, pseudo-determinant, and numerical semigroups

Number Theory 2026-06-29 v1 Combinatorics

Authors: Theo Chinn , Junshu Feng , Stephan Ramon Garcia , Hechun Zhang

Abstract

We investigate matrices with entries in a number field such that some positive power has all its entries in the corresponding ring of integers. Our work generalizes previous results in several directions and we find applications to numerical semigroups.

Cite

@article{arxiv.2606.30876,
  title  = {Power-integral matrices over number fields: the Drazin inverse, pseudo-determinant, and numerical semigroups},
  author = {Theo Chinn and Junshu Feng and Stephan Ramon Garcia and Hechun Zhang},
  journal= {arXiv preprint arXiv:2606.30876},
  year   = {2026}
}

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9 pages