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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On the global dimension of a ring modulo its nilpotent radical


Authors: Ellen Kirkman and James Kuzmanovich
Journal: Proc. Amer. Math. Soc. 102 (1988), 25-28
MSC: Primary 16A60,; Secondary 16A33,16A38
MathSciNet review: 915709
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Abstract: For any preassigned integer $ n \geq 3$, a Noetherian affine PI ring $ R$ is constructed with $ \operatorname{gl dim }R \leq 3$, but $ \operatorname{gl dim}\left( {R/N\left( R \right)} \right) = n$. A second similar ring is constructed with $ \operatorname{gl dim }R \leq 5$ and $ \operatorname{gl dim}\left( {R/N\left( R \right)} \right) = \infty $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0915709-5
PII: S 0002-9939(1988)0915709-5
Article copyright: © Copyright 1988 American Mathematical Society