  In this article, applying the quasi-Gorenstein analogous of the Ulrich's
deformation of certain Gorenstein rings we show that some homological
conjectures, including the Monomial Conjecture, Big Cohen-Macaulay Algebra
Conjecture as well as the Small Cohen-Macaulay Conjecture reduce to the
excellent unique factorization domains. Some other reductions of the Monomial
Conjecture are also proved. We, moreover, show that certain almost complete
intersections adhere the Monomial Conjecture.
