sage: M = cartesian_product((ZZ^2, ZZ^3)); M
The Cartesian product of (Ambient free module of rank 2 over the principal ideal domain Integer Ring, Ambient free module of rank 3 over the principal ideal domain Integer Ring)
sage: M.category()
Category of Cartesian products of modules with basis over (euclidean domains and infinite enumerated sets and metric spaces)
sage: M.base_ring()  # should be Integer Ring