Dictionary

discrete valuation en · NOUN

Meanings

1. (qualifier:field theory) A valuation (on some field) that takes integer values (including infinity).
   • Let k be a field with a nontrivial discrete valuation which is complete and has perfect residue field. 2011, Ricardo Portilla, “Parametrizing nilpotent orbits in p-adic symmetric spaces”, in Robert S. Doran, Paul J. Sally, Jr., Loren Spice, editors, Harmonic Analysis on Reductive, p-adic Groups, American Mathematical Society, page 201:
   • One of the few possibilities to extend some arithmetic aspects of number theory to more abstract fields is via valuation theory and, as a first step, we may restrict attention to discrete valuations. 2004, Farahat S. Aly, Freddy Van Oystaeyen, “Hopf Order Module Algebra Orders”, in Stefaan Caenepeel, Fred Van Oystaeyen, editors, Hopf Algebras in Noncommutative Geometry and Physics, CRC Press, page 21:
   • Therefore the theory branches in two essential parts : first the study of discrete valuations of the Weyl field D#95;1(K) extending a discrete valuation of K, secondly the discrete valuations of D#95;1(K) having the purely transcendental field K(t) as a residue field. 2000, Freddy Van Oystaeyen, Algebraic Geometry for Associative Algebras, CRC Press, page 173:

Forms

Deriveds

discrete valuation field · discrete valuation ring

Relateds

p-adic norm · valuation algebra · valuation domain · p-adic absolute value · residue field · valuation ring