The entanglement of radicals
Chi Wa Chan, Antigona Pajaziti, Flavio Perissinotto, Antonella Perucca
TL;DR
This paper fully characterizes the linear independence of radicals over any field, resolving longstanding mathematical questions about their additive relations and extending Kneser's theorem from 1975.
Contribution
It completes Kneser's theorem on radicals' linear independence and solves a problem posed by Lenstra in 2006.
Findings
Few additive relations among radicals over any field
Complete characterization of radical linear independence
Resolution of a longstanding open problem
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.