  A noncommutative and non-anticommutative quantum field theory is formulated
in a superspace, in which the superspace coordinates satisfy noncommutative and
non-anticommutative relations. A perturbative scalar field theory is
investigated in which only the non-anticommutative algebraic structure is kept,
and one loop diagrams are calculated and found to be finite due to the damping
caused by a Gaussian factor in the propagator.
