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

$$(a\otimes b)({a}^{\prime}\otimes {b}^{\prime})={(1)}^{(\text{deg}b)(\text{deg}{a}^{\prime})}a{a}^{\prime}\otimes b{b}^{\prime}$$ 

where $a,{a}^{\prime},b,{b}^{\prime}$ 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: