Nonfactorizable nonsingular hypercubes (Q1952270)

Hypercubes are generalized (square) matrices and their multiplication generalizes matrix multiplication. The author proves that multiplying nonsingular hypercubes leads to nonsingular hypercubes. He characterizes hypercubes that can be written as a product of other hypercubes. It is shown that the number of nonsingular hypercubes of length 2 over the field of 2 elements is \(3\cdot2^{n-1}\). All of them can be factored. A geometric characterization of nonsingular hypercubes leads to an example of a non-factorisable nonsingular hypercube over the reals. The well-known connection with semifields is mentioned.