If ${\cal U}$ and ${\cal V}$ are ultrafilters on non-empty sets $A$ and $B$ respectively, then the *tensor product* ${\cal U}\otimes{\cal V}$ is the following ultrafilter on $A\times B$:
$$\big\{X\subseteq A\times B: \{a\in A:\{b\in B: (a,b)\in X\}\in {\cal V}\}\in {\cal U}\big\}.$$
It is a standard exercise to verify that this is an ultrafilter on $A\times B$.

We say two non-principal ultrafilters ${\cal U, V}$ are *Rudin-Keisler equivalent* if there is a bijection $\varphi:\omega\to\omega$ such that ${\cal U} =\varphi(\cal V)$, where $\varphi({\cal V}) = \{\varphi(R): R\in {\cal V}\}$.

We say an ultrafilter ${\cal Z}$ on $\omega$ is *Tensor-representable* if there are non-Keisler-Rudin-equivalent ultrafilters ${\cal U}, {\cal V}$ and a bijection $\psi:\omega^2\to \omega$ such that ${\cal Z} =\psi({\cal U}\otimes {\cal V})$.

What is an example of an ultrafilter ${\cal Z}$ on $\omega$ that is not Tensor-representable?