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On a Notion of Cohen-Macaulay and the Non-vanishing of Čech Cohomology Modules
Abstract
In this paper, we study the Cohen-Macaulay property of a general commutative ring with unity defined by Hamilton and Marley. We give sufficient conditions on pullback constructions, fixed rings, and normal monoid rings to all be Cohen-Macaulay in this sense. We also exhibit a class of quasi-local rings where the top Čech cohomology module with respect to a sequence generating the maximal ideal up to radical is non-vanishing.