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    ring isomorphism

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    Suppose F, E are fields and F is a subring of E. Prove that the set of ring isomorphisms Q:E-->E is a group Aut(E) under composition *, and that the set Aut(E/F) of isomorphisms Q in G, with Q(f)=f for all f in F is a subgroup of Aut(E).

    If E is a field and H is a subgroup of Aut(E), show that the set E^H of elements of E that are fixed (sent to themselves) by every Q in H, is a subring of E that is closed under multiplicative inverses - so is a subfield of E

    Show H is a subgroup of Aut(E/E^H) and F is a subgroup of E^Aut(E/F)

    © BrainMass Inc. brainmass.com April 3, 2020, 9:02 pm ad1c9bdddf
    https://brainmass.com/math/ring-theory/set-ring-isomorphisms-356141

    Solution Summary

    This solution provides the steps to prove a given statement about a set of ring isomorphisms.

    $2.19

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