Supermodules
Just as one may generalize vector spaces over a field to modules over a commutative ring, one may generalize super vector spaces over a field to supermodules over a supercommutative algebra (or ring).
A common construction when working with super vector spaces is to enlarge the field of scalars to a supercommutative Grassmann algebra. Given a field K let
denote the Grassmann algebra generated by N anticommuting odd elements θi. Any super vector space over K can be embedded in a module over R by considering the (graded) tensor product
Read more about this topic: Super Vector Space