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HOMOLOGICAL PROPERTIES OF FULLY BOUNDED NOETHERIAN RINGS

Published online by Cambridge University Press:  01 February 1997

KOK-MING TEO
KOK-MING TEO
Affiliation:
Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260. E-mail: [email protected]
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Abstract

Let R be a fully bounded Noetherian ring of finite global dimension. Then we prove that K dim (R) [les ] gldim (R). If, in addition, R is local, in the sense that R/J(R) is simple Artinian, then we prove that R is Auslander-regular and satisfies a version of the Cohen–Macaulay property. As a consequence, we show that a local fully bounded Noetherian ring of finite global dimension is isomorphic to a matrix ring over a local domain, and a maximal order in its simple Artinian quotient ring.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 55 , Issue 1 , February 1997 , pp. 37 - 54
Copyright
The London Mathematical Society 1997

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