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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
DOI: https://doi.org/10.1090/S0002-9939-1991-1057944-4
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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Article copyright: © Copyright 1991 American Mathematical Society