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A coherent array of regenerative amplifiers in an external cavity with a rank 1 scattering matrix is described and analyzed. Using a resonant cavity analysis, it is shown how the addition of regenerative feedback to each element in the array creates a phase shift relative to the well-known “cold-cavity phase shift”. This phase shift is quantified and found to significantly affect the phasing properties of coherent arrays, even in the absence of the nonlinear Kerr effect and the gain-dependent phase shift. In particular, this regenerative phase shift is shown to concentrate the distribution of phases at the output of the laser array into a narrower phase range compared to the random distribution expected using a nonregenerative amplifier in the presence of effectively random cold-cavity phase shifts.