Stickelberger's discriminant theorem for algebras

Asher Auel; Owen Biesel; John Voight

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arXiv · 2208.06138

Stickelberger's discriminant theorem for algebras

Asher Auel·Owen Biesel·John Voight

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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.

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Asher Auel, Owen Biesel, John Voight. 2022-08-12. Stickelberger's discriminant theorem for algebras. https://arxiv.org/abs/2208.06138

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