A note on Noetherian P.I. rings

Braun, Amiram

doi:10.1090/S0002-9939-1981-0630034-1

A note on Noetherian P.I. rings
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by Amiram Braun

Proc. Amer. Math. Soc. 83 (1981), 670-672

DOI: https://doi.org/10.1090/S0002-9939-1981-0630034-1

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Abstract:

Let $R = F\{ {x_1}, \ldots ,{x_k}\}$ be an affine semiprime p.i. ring, Krull-$\dim (R) = 2$ and $F$ a central subfield. It is proved that $R$ is noetherian iff $R$ is a left (right) finite module over a commutative affine subring.

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