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We make a numerical study of decoherence on the teleportation algorithm implemented in a linear chain of three nuclear spins system. We study different types of environments, and we determine the associated decoherence time as a function of the dissipative parameter. We found that the dissipation parameter to get a well defined quantum gates (without significant decoherence) must be within the range of γ≤4×10-4 for not thermalized case, which was determined by using the purity parameter calculated at the end of the algorithm. For the thermalized case the decoherence is stablished for very small dissipation parameter, making almost not possible to implement this algorithm for not zero temperature.