标题： 某些同调猜想约化到优良的唯一因子分解环 显示英文标题

标题： Reduction of some homological conjectures to excellent unique factorization domains

摘要： 本文中，利用某些Gorenstein环的Ulrich变形的拟Gorenstein类似方法，我们证明了一些同调猜想，包括Monomial猜想、Big Cohen-Macaulay代数猜想以及Small Cohen-Macaulay猜想可以归约到优良的唯一因子分解环上。我们也证明了Monomial猜想的某些其他归约。此外，我们还证明了某些几乎完全交环满足Monomial猜想。 显示英文摘要

摘要： 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.