  In the article "Non-commutative Grobner bases for commutative algebras",
Eisenbud-Peeva-Sturmfels proved a number of results regarding Grobner bases and
initial ideals of those ideals in the free associative algebra which contain
the commutator ideal. We prove similar results for ideals which contains the
anti-commutator ideal (the defining ideal of the exterior algebra). We define
one notion of generic initial ideals in the free assoicative algebra, and show
that gin's of ideals containing the commutator ideal, or the anti-commutator
ideal, are finitely generated.
