Maximal ideals in Laurent polynomial rings
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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.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- 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