Subrings of Noetherian rings
Authors:
Edward Formanek and Arun Vinayak Jategaonkar
Journal:
Proc. Amer. Math. Soc. 46 (1974), 181186
MSC:
Primary 16A46
MathSciNet review:
0414625
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Abstract: Let be a subring of a ring such that is a finitely generated right module. Clearly, if is a right Noetherian ring then so is . Generalizing a result of P. M. Eakin, we show that if is right Noetherian and is commutative then is Noetherian. We also show that if has a finite generating set such that for , then a right module is Noetherian, Artinian or semisimple iff it is respectively so as a right module. This yields a result of Clifford on group algebras.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197404146255
PII:
S 00029939(1974)04146255
Keywords:
Commutative Noetherian rings,
noncommutative Noetherian rings,
P. I. rings,
Eakin's theorem,
Clifford's theorem on group algebras
Article copyright:
© Copyright 1974
American Mathematical Society
