Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Education
A Theory Of Non-Noetherian Gorenstein Rings, Livia M. Miller
A Theory Of Non-Noetherian Gorenstein Rings, Livia M. Miller
Department of Mathematics: Dissertations, Theses, and Student Research
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 Cech 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 FP-injective dimension as defined by Stenstrom is also explored. Finally, an additional characterization of Gorenstein rings involving homological dimensions is examined …