Hilbert 90 for Algebras with Conjugation
Patrik Lundstr\"om

TL;DR
This paper extends Hilbert 90 to a broad class of non-commutative, non-associative algebras, enabling parametrization of solutions to norm one equations in ordered fields.
Contribution
It introduces a generalized version of Hilbert 90 applicable to complex algebraic structures, including iterated Conway-Smith doublings.
Findings
Generalized Hilbert 90 for non-commutative algebras
Parametrization of norm one solutions in ordered fields
Applicable to iterated algebraic constructions
Abstract
We show a version of Hilbert 90 that is valid for a large class of algebras many of which are not commutative, distributive or associative. This class contains the nth iteration of the Conway-Smith doubling procedure. We use our version of Hilbert 90 to parametrize all solutions in ordered fields to the norm one equation for such algebras.
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Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Topics in Algebra · Matrix Theory and Algorithms
