Maximal ideals in Laurent polynomial rings

Nashier, Budh

doi:10.1090/S0002-9939-1992-1086336-8

Maximal ideals in Laurent polynomial rings
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Proc. Amer. Math. Soc. 115 (1992), 907-913 Request permission

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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Efficient generation of zero dimensional ideals in polynomial and Laurent polynomial rings