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Math Help - Ring Homomorphism

  1. #1
    Junior Member hercules's Avatar
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    Ring Homomorphism

    Prove that if F is a field, R is a ring, and \theta :F\rightarrow R is a ring homomorphism, then either \theta is one to one or  \theta(a)=0 for all a in F.

    i'm stuck on this proof.

    Thank you.
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  2. #2
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    Quote Originally Posted by hercules View Post
    Prove that if F is a field, R is a ring, and \theta :F\rightarrow R is a ring homomorphism, then either \theta is one to one or  \theta(a)=0 for all a in F.
    Hint: \ker \theta is an ideal of F.
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