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In this paper, we compute an achievable rate of a Gaussian Z-interference channel as shown in Fig. 1, when transmit node C has causal, imperfect cognitive knowledge of the signal sent by transmit node A. This achievable rate is derived using a two-phase transmission scheme in which node C uses a combination of a linear minimum mean square error (LMMSE) estimator and dirty paper code and node D employs a combination of LMMSE estimator and partial interference canceler. Numerical results indicate that the achievable rate of the Gaussian Z-interference channel increases significantly with cognition under certain channel conditions. We also derive an upper bound on the capacity of this channel with cognition and quantify the channel conditions under which the proposed achievable scheme equals the upper bound.