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In this paper we exploit some general results on the tensor product of free resolutions to deduce important new algebraic properties of biregular functions on 2n quaternionic functions. In particular we are able to construct a minimal resolution for the associated module and we are able to compute all the relevant graded Betti numbers.doi:10.1080/17476930500482515 fatcat:4p6rpsq4xbelhctowwghi6t2vq