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

 

The Noetherian property for quotient rings of infinite polynomial rings


Authors: Robert Gilmer and William Heinzer
Journal: Proc. Amer. Math. Soc. 76 (1979), 1-7
MSC: Primary 13B25
MathSciNet review: 534377
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Abstract: Let X be an infinite set of indeterminates over the commutative Noetherian ring R with identity. We prove that the quotient ring of $ R[X]$ with respect to the multiplicative system of polynomials of unit content is also Noetherian. Moreover, we show that certain quotient rings of $ R[X]$ with respect to multiplicative systems of monic polynomials (where ``monic'' is appropriately defined) are also Noetherian.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0534377-2
PII: S 0002-9939(1979)0534377-2
Keywords: Noetherian ring, polynomial of unit content, monic polynomial
Article copyright: © Copyright 1979 American Mathematical Society