On the global dimension of a ring modulo its nilpotent radical

Kirkman, Ellen; Kuzmanovich, James

doi:10.1090/S0002-9939-1988-0915709-5

On the global dimension of a ring modulo its nilpotent radical
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Proc. Amer. Math. Soc. 102 (1988), 25-28 Request permission

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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