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Rendiconti del Circolo Matematico di Palermo

, Volume 54, Issue 3, pp 396–408 | Cite as

A field-theoretic invariant for domains

  • David E. Dobbs
Article

Abstract

SoientRT des anneaux intègres. D’après Dobbs-Mullins, on pose Λ(T/R) ≔ sup{λ(k Q (T)/k QR (R)) |Q ∈ Spec(T)} où, pour des corpsKL,λ(L/K) est la longueur maximale d’une chaîne de corps contenus entreK etL. On introduitσ(R):=sup{Λ(T/R)|T est un suranneau deR\. On détermineσ(R) siR′, la clôture intégrale deR, est un anneau de Prüfer et également siR est un anneau de pseudo-valuation. On considère le cas oùσ(R)=1, en particulier siR′ est une extension minimale deR. Plusieurs calculs sont facilités par un résultat sur les carrés cartésiens, et il y a des exemples divers.

Keywords

Prime Ideal Maximal Ideal Commutative Ring Cardinal Number Integral Closure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TennesseeKnoxville

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