Alberto Gioia

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math.AC2016

Isomorphisms of Discriminant Algebras

Owen Biesel, Alberto Gioia

For each natural number $n$ , we define a category whose objects are discriminant algebras in rank $n$ , i.e. functorial means of attaching to each rank- $n$ algebra a quadratic algeb…

math.AC2015

A new discriminant algebra construction

Owen Biesel, Alberto Gioia

A discriminant algebra operation sends a commutative ring $R$ and an $R$ -algebra $A$ of rank $n$ to an $R$ -algebra $Δ_{A / R}$ of rank $2$ with the same discriminant bilinear form. C…

math.AC2015

The Galois closure for rings and some related constructions

Alberto Gioia

Let $R$ be a ring and let $A$ be a finite projective $R$ -algebra of rank $n$ . Manjul Bhargava and Matthew Satriano have recently constructed an $R$ -algebra $G (A / R)$ , the Galois clo…