The cohomology rings of smooth toric varieties and quotients of moment-angle complexes

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