  Gelfand, Retakh, Serconek and Wilson, in \cite{GRSW}, defined a graded
algebra $A_\Gamma$ attached to any finite ranked poset $\Gamma$ - a
generalization of the universal algebra of pseudo-roots of noncommutative
polynomials. This algebra has since come to be known as the splitting algebra
of $\Gamma$. The splitting algebra has a secondary filtration related to the
rank function on the poset and the associated graded algebra is denoted here by
$A'_\Gamma$. We calculate the cohomology algebra (and coalgebra) of $A'_\Gamma$
explicitly. As a corollary to this calculation we have a proof that $A'_\Gamma$
is Koszul (respectively quadratic) if and only if $\Gamma$ is Cohen-Macaulay
(respectively uniform). We show by example that the cohomology algebra (resp.
coalgebra) of $A_\Gamma$ may be strictly smaller that the cohomology algebra
(resp. coalgebra) of $A'_\Gamma$.
