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

 

A two-dimensional non-Noetherian factorial ring


Author: Robert Gilmer
Journal: Proc. Amer. Math. Soc. 44 (1974), 25-30
MSC: Primary 13F15
MathSciNet review: 0335500
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Abstract: Let $ R$ be a commutative ring with identity and let $ G$ be an abelian group of torsion-free rank $ \alpha $. If $ \{ {X_\lambda }\} $ is a set of indeterminates over $ R$ of cardinality $ \alpha $, then the group ring of $ G$ over $ R$ and the polynomial ring $ R[\{ {X_\lambda }\} ]$ have the same (Krull) dimension. The preceding result and a theorem due to T. Parker and the author imply that for each integer $ k \geqq 2$, there is a $ k$-dimensional non-Noetherian unique factorization domain of arbitrary characteristic.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0335500-0
PII: S 0002-9939(1974)0335500-0
Keywords: Unique factorization domain, group ring, Noetherian ring
Article copyright: © Copyright 1974 American Mathematical Society