  A classification of all four-dimensional power-commutative real division
algebras is given.
  It is shown that every four-dimensional power-commutative real division
algebra is an isotope of a particular kind of a quadratic division algebra. The
description of such isotopes in dimension four and eight is reduced to the
description of quadratic division algebras. In dimension four this leads to a
complete and irredundant classification. As a special case, the
finite-dimensional power-commutative real division algebras that have a unique
non-zero idempotent are characterised.
