If $A$ and $B$ are $\mathbb{Z}$ -graded algebras, we define the graded tensor product (or super tensor product) $A \otimes_{su} B$ to be the ordinary tensor product as graded modules, but with multiplication - called the super product - defined by $$(a \otimes b)(a' \otimes b') = (-1)^{(\text{deg \ } b)(\text{deg \ } a')}aa' \otimes bb'$$ where $a,a',b,b'$ are homogeneous. The super tensor product of $A$ and $B$ is itself a graded algebra, as we grade the super tensor product of $A$ and $B$ as follows:

$$ (A \otimes_{su} B)^n = \coprod_{p,q \text{ : } p + q = n} A^p \otimes B^q $$