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Results tagged with quaternions
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user 12858
4
votes
Accepted
Subfields of division rings of degree $2$ which are not invariant
(This is basically a more detailed version of Eoin's comment.)
I assume that you are considering division algebras over a field $k$, i.e., $Z(A) = k$. If $B$ is a subalgebra of dimension $2$ of $A$, t …
- 6,614
7
votes
How to prove that a quaternion algebra over ℤₚ is isomorphic to Mat₂(ℤₚ) for p prime?
At the risk of being redundant and repeating earlier answers, let me mention that this is explicitly contained in the book "Elementary number theory, group theory and Ramanujan graphs" by Davidoff, Sa …
- 6,614
3
votes
2
answers
919
views
Skew fields inside quaternion division algebras
Suppose that $Q$ is a quaternion division algebra with center $k$, where $k$ is an arbitrary commutative field (let's say with $\operatorname{char}(k) \neq 2$ if necessary). Assume that $D$ is an arbi …
- 6,614