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

 

Henselian rings and Weierstrass polynomials


Author: Budh Nashier
Journal: Proc. Amer. Math. Soc. 112 (1991), 685-690
MSC: Primary 13F20; Secondary 13B25, 13J15
MathSciNet review: 1057944
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Abstract: We give two characterizations of a one-dimensional Henselian domain. If $ \left( {A,\mathcal{M}} \right)$ is a local domain of Krull dimension at least two, or if $ \left( {A,\mathcal{M}} \right)$ is a one-dimensional Henselian local domain, then a polynomial $ f$ in $ A\left[ T \right]$ is Weierstrass if and only if $ \left( {\mathcal{M},T} \right)$ is the only maximal ideal of $ A\left[ T \right]$ that contains $ f$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1057944-4
PII: S 0002-9939(1991)1057944-4
Article copyright: © Copyright 1991 American Mathematical Society