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

 

Finite extensions of rings


Authors: Barbara Cortzen and Lance W. Small
Journal: Proc. Amer. Math. Soc. 103 (1988), 1058-1062
MSC: Primary 16A38; Secondary 16A21, 16A33, 16A56
MathSciNet review: 954983
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Abstract: The paper concerns some cases of ring extensions $ R \subset S$, where $ S$ is finitely generated as a right $ R$-module and $ R$ is right Noetherian. In $ {\text{\S}}1$ it is shown that if $ R$ is a Jacobson ring, then so is $ S$, with the converse true in the $ {\text{PI}}$ case. In $ {\text{\S}}2$ we show that if $ S$ is semiprime $ {\text{PI}}$, $ R$ must also be left (as well as right) Noetherian and $ S$ is finitely generated as a left .$ R$-module. $ {\text{\S}}3$ contains a result on $ E$-rings.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0954983-6
PII: S 0002-9939(1988)0954983-6
Article copyright: © Copyright 1988 American Mathematical Society