Multiplicative quadratic maps
Matthias Gr\"uninger

TL;DR
This paper characterizes multiplicative quadratic maps between rings and fields, showing they are induced by homomorphisms or composition algebras, and establishes a multiplicative version of Artin's Theorem for uniqueness.
Contribution
It provides a complete classification of multiplicative quadratic maps, revealing their structure and uniqueness properties in the context of rings and fields.
Findings
Multiplicative quadratic maps are induced by homomorphisms or composition algebras.
When K is a field, such maps are products of two field homomorphisms.
A multiplicative version of Artin's Theorem proves the uniqueness of these maps up to multiplicity.
Abstract
In this paper we prove that a multiplicative quadratic map between a unital ring and a field is induced by a homomorphism from into or a composition algebra over . Especially we show that if 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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras · Finite Group Theory Research
