English

The entanglement of radicals

Number Theory 2025-08-27 v1

Abstract

In this work we achieve a full understanding of the so-called entanglement of radicals, showing that over any field there are extremely few additive relations among radicals. Our results complete a famous theorem by Kneser from 1975 on the linear independence of radicals and solve a problem discussed by Lenstra in 2006.

Keywords

Cite

@article{arxiv.2508.19211,
  title  = {The entanglement of radicals},
  author = {Chi Wa Chan and Antigona Pajaziti and Flavio Perissinotto and Antonella Perucca},
  journal= {arXiv preprint arXiv:2508.19211},
  year   = {2025}
}