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Math Help - integral domain?

  1. #1
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    integral domain?

    Im having problems workout out
    For which n are the integers mod n an integral domain?

    can any1 show me how to prove this
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kbartlett View Post
    Im having problems workout out
    For which n are the integers mod n an integral domain?

    can any1 show me how to prove this
    ok, lets start with the basics. do you know what an integral domain is?
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  3. #3
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    Quote Originally Posted by kbartlett View Post
    Im having problems workout out
    For which n are the integers mod n an integral domain?
    For \mathbb{Z}_n we require that if [a]_n[b]_n = [0]_n implies [a]_n=[0]_n or [b]_n=[0]_n.

    Now if n is not prime there is 1 < d < n so that d|n. Then [d]_n [n/d]_n = [0]_n but neither [d]_n,[n/d]_n are identity elements.

    Therefore n must be prime.
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  4. #4
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    Lol im so stuipd, it was already in my lecture notes anyway.

    But thanks
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