Homological Properties of Fully Bounded Noetherian Rings |
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Authors: | Teo Kok-Ming |
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Institution: | Department of Mathematics, National University of Singapore 10 Kent Ridge Crescent, Singapore 119260. E-mail: matteokm{at}math.nus.sg |
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Abstract: | Let R be a fully bounded Noetherian ring of finite global dimension.Then we prove that K dim (R) gldim (R). If, in addition, Ris local, in the sense that R/J(R) is simple Artinian, thenwe prove that R is Auslander-regular and satisfies a versionof the CohenMacaulay property. As a consequence, we showthat a local fully bounded Noetherian ring of finite globaldimension is isomorphic to a matrix ring over a local domain,and a maximal order in its simple Artinian quotient ring. |
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