Multiplicative quadratic maps

Abstract

In this paper we prove that a multiplicative quadratic map between a unital ring K and a field L is induced by a homomorphism from K into L or a composition algebra over L. Especially we show that if K is a field, then every multiplicative quadratic map is the product of two field homomorphisms. Moreover, we prove a multiplicative version of Artin's Theorem showing that a product of field homomorphisms is unique up to multiplicity.

Boundary Moufang trees with abelian root groups of characteristic p

“…Corollary 2.9 (Corollary 1.3 in [Grü14a]). Let K, L be commutative fields, and q : K → L be a multiplicative quadratic map.…”

“…We recall from [Grü14a] that a multiplicative quadratic map is a map q : K → L between two unital rings satisfying the following conditions:…”