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A theory of non-Noetherian Gorenstein rings

Livia M Miller, University of Nebraska - Lincoln


In Noetherian rings there is a hierarchy among regular, Gorenstein and Cohen-Macaulay rings. Regular non-Noetherian rings were originally defined by Bertin in 1971. In 2007, Hamilton and Marley used C˘ech cohomology to introduce a theory of Cohen-Macaulay for non-Noetherian rings, answering a question posed by Glaz. This dissertation provides a theory of non-Noetherian Gorenstein rings agreeing with the Noetherian definition, and for which regular rings are Gorenstein, and coherent Gorenstein rings are Cohen-Macaulay. The relationship between Gorenstein rings and F P-injective dimension as defined by Stenström is also explored. Finally, an additional characterization of Gorenstein rings involving homological dimensions is examined in the non-Noetherian case. ^

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Recommended Citation

Miller, Livia M, "A theory of non-Noetherian Gorenstein rings" (2008). ETD collection for University of Nebraska - Lincoln. AAI3315051.