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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Rings of polynomials


Authors: A. Evyatar and A. Zaks
Journal: Proc. Amer. Math. Soc. 25 (1970), 559-562
MSC: Primary 13.93
DOI: https://doi.org/10.1090/S0002-9939-1970-0258820-3
MathSciNet review: 0258820
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Abstract: For an algebra $ R$ over a field $ k$, with residue field $ K$ to be a ring of polynomials in one variable over $ k$ it is necessary that $ \operatorname{tr} \cdot \deg \;K/k = 1$. We prove that under the hypothesis $ \operatorname{tr} \cdot \deg \;K/k = 1$ is a ring of Krull-dimension at most one. This is used to derive sufficient conditions for $ R$ to be a ring of polynomials in one variable over $ k$.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0258820-3
Keywords: Rings of polynomials, rings of power series, unique factorization domain, principal ideal domain, Euclidean domain, transcendence degree, Krull dimension
Article copyright: © Copyright 1970 American Mathematical Society

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