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Finite Cohen–Macaulay Type and Smooth Non-Commutative Schemes
Published online by Cambridge University Press: 20 November 2018
Abstract
A commutative local Cohen–Macaulay ring $R$ of finite Cohen–Macaulay type is known to be an isolated singularity; that is, $\text{Spec}(R)\backslash \{m\}$ is smooth. This paper proves a non-commutative analogue. Namely, if $A$ is a (non-commutative) graded Artin–Schelter Cohen–Macaulay algebra which is fully bounded Noetherian and has finite Cohen–Macaulay type, then the non-commutative projective scheme determined by $A$ is smooth.
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- Copyright © Canadian Mathematical Society 2008
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