  In a recent preprint, Ilse Fischer and Martina Kubitzke, proved the
bilinearity of the Segre transform under some restricted hypothesis, motivated
by their results we show in this paper the bilinearity of the Segre transform
in general. We apply these results to compute the postulation number of a
series. Our second application is motivated by the paper of David A. Cox, and
Evgeny Materov (2009), where is computed the Castelnuovo-Mumford regularity of
the Segre Veronese embedding, we can extend partially their result and compute
the Castelnuovo-Mumford regularity of the Segre product of Cohen-Macaulay
modules.
