Exact discretization of non-commutative space-time

Non-commutative space-time is discussed for discrete case. An exact discretization of the non-commutative space-time is proposed. New discrete operators, which satisfy the same algebraic relations as standard derivatives of integer orders, are used. Exact discretization of the non-commutative space-time is suggested by using generalization of the star-product (the Moyal-Weyl product) based on the recently proposed exact finite differences. The suggested discrete non-commutative space-time corresponds to the standard "continuous" non-commutative space-time without any approximations. The suggested discrete non-commutative space-time can be interpreted as a special physical (crystal) lattice with long-range interaction.