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Math Help - automorphism mappings

  1. #1
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    automorphism mappings

    Let R be ring, I ideal of R
    Let f is automorphism of R.
    let say: (f(x)+4 )f(y)=0, \forall x,y \in I
    if i say {f}^{-1 } (f(x)+4 ) y = 0, \forall x,y \in

    whether the statement was valid?
    if yes, any reason to explain that? (i know f is invertible cause f is 1-1, but whether there is a more specific explanation?)
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  2. #2
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    i don't see anything wrong with that.

    since f^{-1} is also an automorphism, you can even say that (x + f^{-1}(4))y = 0 for all x,y in I.
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