Stickelberger's discriminant theorem for algebras
Number Theory
2022-09-20 v2 Combinatorics
Rings and Algebras
Abstract
Stickelberger proved that the discriminant of a number field is congruent to 0 or 1 modulo 4. We generalize this to an arbitrary (not necessarily commutative) ring of finite rank over the integers using techniques from linear algebra. Our proof, which relies only on elementary matrix identities, is new even in the classical case.
Keywords
Cite
@article{arxiv.2208.06138,
title = {Stickelberger's discriminant theorem for algebras},
author = {Asher Auel and Owen Biesel and John Voight},
journal= {arXiv preprint arXiv:2208.06138},
year = {2022}
}
Comments
15 pages; accepted to Amer. Math. Monthly