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Math Help - isomorphism

  1. #1
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    isomorphism

    Show that S={0, 4, 8, 12, 16, 20, 24} is a subring of Z28. Then prove that the map of f:Z7 onto S is given by f([x]7)=[8x]28 is an isomorphism.

    I understand the subring part of the statement and have already proved that. But I do not understand how to prove the second statement.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by empressA View Post
    Show that S={0, 4, 8, 12, 16, 20, 24} is a subring of Z28. Then prove that the map of f:Z7 onto S is given by f([x]7)=[8x]28 is an isomorphism.

    I understand the subring part of the statement and have already proved that. But I do not understand how to prove the second statement.
    Prove that it is a bijective mapping which is a ring homomorphism ( f(xy)=f(x)f(y),\text{ }f(x+y)=f(x)+f(y))
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  3. #3
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    Thank you..i understand what you are saying and I got it..
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