  There are two types of non(anti-)commutative deformation of D=4, N=1
supersymmetric field theories and D=2, N=2 theories. One is based on the
non-supersymmetric star product and the other is based on the supersymmetric
star product . These deformations cause partial breaking of supersymmetry in
general. In case of supersymmetric star product, the chirality is broken by the
effect of the supersymmetric star product, then it is not clear that lagrangian
or observables including F-terms preserve part of supersymmetry. In this
article, we investigate the ring structure whose product is defined by the
supersymmetric star product. We find the ring whose elements correspond to 1/2
SUSY F-terms. Using this, the 1/2 SUSY invariance of the Wess-Zumino model is
shown easily and directly.
