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Math Help - Ring

  1. #1
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    Ring

    I am also having trouble proving this statement:

    Let R be a commutative ring which is not a domain. Then R has no units other that 1 and -1. Is this true or is Zp a counterexample.
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  2. #2
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    Quote Originally Posted by chadlyter View Post
    Then R has no units other that 1 and -1.
    False. Consider Z_m where m is not a prime and m>1.
    This is not an integral domain. However the units are the numbers relatively prime to m.

    Is this true or is Zp a counterexample.
    No. Z_p is an integral domain. How can it be a counterexample?
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