Consider a tangent bundle with even and odd parts $T_0 + T_1$, define a space $\Omega^{k,l}_{p,q}$ consisting of (p,q)-forms taking values in $\wedge^k T_0 \otimes \wedge^l T_1$, i.e. the space of $(p,q)$-forms which are also $(k,l)$-multivectors.
Now to compute a direct sum of $\lambda + \rho$, where $\lambda \in \Omega^{k,0}_{p,q}$ and $\rho \in \Omega^{k,1}_{0,q}$, we need $\lambda$ and $\rho$ to be over the same polynomial ring. Any tips?