We consider on-commutative space- time and give a brief review on the non-commutative standard model(NCSM). There are two approaches to construct the NCSM. The first one based on the SU(3)×SU(2) ×U(1) gauge group and the number of particles are the same with the ordinary standard model. In this approach the NC-fields depend on the NC-parameter via the Seiberg-Witten maps. Meanwhile the second approach based on the U(3)×U(2)×U(1) gauge group leads to the ordinary gauge group for the standard model through the spontaneous gauge symmetry breaking in two steps. In this model there are new particles with respect to the ordinary standard model and the NC-fields does not depend on the NC-parameter. In this thesis we examine the decay of the Z-gauge boson to the quark-antiquark channel considering the earth rotation in the first approach of the NCSM. The latitude dependence of the decay rate provides a test on the non-commutativity in future measurements on the Z-decay in different places. We show that bound on the parameter of non-commutativity of the order of 100GeV. Keywords : Non-commutative space- time، NC-parameter، Seiberg-Witten maps.
