What specific algebraic properties are broken at each Cayley-Dickson stage beyond octonions?
84183
Why are properties lost in the Cayley–Dickson construction?
78307
Under what conditions is $AA^T$ invertible?
99585
Do the non-zero eigenvalues of AB and BA have the same algebraic multiplicity (for AB and BA not square)?
127198
What is $\mathbb{C}^{Aut(\mathbb{C}/\mathbb{Q})}$?
67796
How to prove that the algebra $k[x, xy, xy^2, xy^3, \dotsc]$ is not finitely generated?
91756
Degeneracy in one dimension
132725
Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
100720
Negative quotients and their remainders
26764
Proving that $\mathbb R^3$ cannot be made into a real division algebra (and that extending complex multiplication would not work)
42213
Computing $\text{Gal}(\mathbb{Q}^{ab}/\mathbb{Q})$
11862
Reconstruction of "wavefunction" phases from $|\psi(x)|$ and $|\tilde \psi(p)|$
68211
Characters of Symmetric and Antisymmetric Powers
86308
Yoneda-Lemma as generalization of Cayley`s theorem?
46144
Understanding imaginary exponents
124864
A not free $\mathbb{Z}$-module
117266
Supersymmetry calculations using computer algebra
47173
Half-integer eigenvalues of orbital angular momentum