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. I am going to explain that their formula gives the correct cup product if 2 is invertible in the chosen coefficient ring, but not in general. I will rectify this by defining an explicit deformation of the canonical multiplication on the torsion product. A sketch of the proof will be given in the following lecture.