  Assuming the Generalized Continuum Hypothesis, this paper answers the
question: when is the tensor product of two ultrafilters equal to their
Cartesian product? It is necessary and sufficient that their Cartesian product
is an ultrafilter; that the two ultrafilters commute in the tensor product;
that for all cardinals $\lambda$, one of the ultrafilters is both
$\lambda$-indecomposable and $\lambda^+$-indecomposable; that the ultrapower
embedding associated to each ultrafilter restricts to a definable embedding of
the ultrapower of the universe associated to the other.
