Cayley–Dickson algebras form an infinite sequence of non-associative algebras starting with the reals, complexes, quaternions, and octonions, and the annihilators of their elements quantify the zero-divisor structure.
The annihilator of any element in the 2ⁿ-dimensional Cayley–Dickson algebra has dimension at most 2ⁿ − 4n + 4.
Every multiple of four between 0 and that upper bound occurs as some annihilator's dimension — a theorem of Moreno — and the zero divisors with maximal annihilator are completely described.