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Extention field

  1. Oct 20, 2007 #1
    let K be an extention field of L and L be an extenstion field of F.

    (1) t(a)=a ,for all t e G(K,F)

    (2) t(a)=a ,for all t e G(L,F)

    where e means "belongs to" , G(K,F) means "set of all automorphisms of K

    leaving every element of F fixed and similarly for G(L,F).

    i would like to know is (2) implies (1) or (1) implies (2)?

    i think (2) implies (1) but not sure.[i have used simple logic no.of automorphisms of K =< no.of auto. of L]

    if not then please give answer with counter example,if there no relation between

    them then explain with reasion.

    thanks in advanced for help me
  2. jcsd
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