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.
In this paper several quasi-Gorenstein counterparts to some known properties of Gorenstein rings are given. We, furthermore, give an explicit description of the attached prime ideals of certain local cohomology modules.2010 Mathematics Subject Classification. 13H10, 13D45.
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