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Maximal ideals in Laurent polynomial rings


Author: Budh Nashier
Journal: Proc. Amer. Math. Soc. 115 (1992), 907-913
MSC: Primary 13F20; Secondary 13J15
DOI: https://doi.org/10.1090/S0002-9939-1992-1086336-8
MathSciNet review: 1086336
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Abstract: We prove, among other results, that the one-dimensional local domain $ A$ is Henselian if and only if for every maximal ideal $ M$ in the Laurent polynomial ring $ A[T,{T^{ - 1}}]$, either $ M \cap A[T]$ or $ M \cap A[{T^{ - 1}}]$ is a maximal ideal. The discrete valuation ring $ A$ is Henselian if and only if every pseudoWeierstrass polynomial in $ A[T]$ is Weierstrass. We apply our results to the complete intersection problem for maximal ideals in regular Laurent polynomial rings.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1086336-8
Article copyright: © Copyright 1992 American Mathematical Society

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