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A generalized fundamental principle
Author(s) -
Khanduja Sudesh K.,
Saha Jayanti
Publication year - 1999
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300007580
Subject(s) - mathematics , residue field , algebraic closure , valuation (finance) , algebraic number , pure mathematics , field (mathematics) , discrete mathematics , mathematical analysis , differential equation , differential algebraic equation , ordinary differential equation , finance , economics
Let ν be a rank 1 henselian valuation of a field K having unique extension ῡ to an algebraic closureK ¯of K . For any subextension L/K ofK ¯ / K , let G ( L ), Res ( L ) denote respectively the value group and the residue field of the valuation obtained by restricting ῡ to L . If a ∈ K ¯ \ K defineδ K ( a ) = sup { v ¯ ( a − c ) | c ∈ K ¯ , [ K ( c ) : K ] < [ K ( a ) : K ] } ,ω K ( a ) = max { v ¯ ( a − a ′ ) | a ′ ≠ a runs over K ‐ conjugates of a } .