  Partial quotients of moment-angle complexes are topological analogues of
smooth, not necessarily compact toric varieties. In 1998, Buchstaber and Panov
proposed a formula for the cohomology ring of such a partial quotient in terms
of a torsion product involving the corresponding Stanley-Reisner ring. We show
that their formula gives the correct cup product if 2 is invertible in the
chosen coefficient ring, but not in general. We rectify this by defining an
explicit deformation of the canonical multiplication on the torsion product.
