  We investigate cohomological gauge theories in noncommutative R^{2D}. We show
that vacuum expectation values of the theories do not depend on noncommutative
parameters, and the large noncommutative parameter limit is equivalent to the
dimensional reduction. As a result of these facts, we show that a partition
function of a cohomological theory defined in noncommutative R^{2D} and a
partition function of a cohomological field theory in R^{2D+2} are equivalent
if they are connected through dimensional reduction. Therefore, we find several
partition functions of supersymmetric gauge theories in various dimensions are
equivalent. Using this technique, we determine the partition function of the
N=4 U(1) gauge theory in noncommutative R^4, where its action does not include
a topological term. The result is common among (8-dim, N=2), (6-dim, N=2),
(2-dim, N=8) and the IKKT matrix model given by their dimensional reduction to
0-dim.
