Quantifier Elimination and Invariant Theory: Applications to Quaternions, Octonions, and Other Algebras
Abstract
We build on our previous paper \cite{constructive} by using the general method introduced there in conjunction with invariant theory. This yields quantifier elimination results for the classical quaternions, octonions, as well as other classes of finite-dimensional algebras over real closed and algebraically closed fields. In particular, the first two examples answer an open question posed recently in \cite{savi}.
Fields of Study & Subjects
Polynomial and algebraic computation
Algebraic Geometry and Number Theory
Rings
Modules
and Algebras
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 24 February 2026
- Language
- EN
- Document type
- Preprint