5
votes
0answers
175 views

Hermitian forms over quaternion algebra

Notations: Let $Q=(a,b)$ be a quaternion algebra over a field of characteristic $\neq 2$, i.e. $i^2=a, j^2=b, k=ij, ij=-ji$. Consider $K=k(t)(\alpha)$, where $\alpha=\sqrt{at^2+b}$. Let ...
1
vote
0answers
178 views

(Non-)existence of skew fields satisfying a SGPI (=skew generalized polynomial identity)

Let $K$ be a skew-field, infinite dimensional over its center $F$. From Kaplansky's PI-theorem it then follows that $K$ cannot satisfy a polynomial identity (the theorem says that primitive ...