A Quaternionic Nullstellensatz

TL;DR

This paper establishes a Nullstellensatz for polynomial functions over quaternions and characterizes polynomial identities in division algebras, extending classical algebraic results to non-commutative settings.

Contribution

It introduces a Nullstellensatz for quaternionic polynomial functions and characterizes polynomial identities in division algebras, expanding algebraic theory to non-commutative contexts.

Findings

Proves a Nullstellensatz for quaternionic polynomial functions.

Characterizes polynomial identities over quaternions and division algebras.

Extends classical algebraic results to non-commutative division algebras.

Abstract

We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's ring of real quaternions. We also characterize the generalized polynomial identities in n variables which hold over the quaternions, and more generally, over any division algebra.