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Math Help - Principal Ideals

  1. #1
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    Principal Ideals

    How can I prove that every ideal of Zn is principal?

    I've proved that if K is an ideal of Zn that contains an element k then it contains all the elements of the form mk (m in Zn)...But how can I prove that there are no elements that are not of the form mk?


    THanks!
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by WannaBe View Post
    How can I prove that every ideal of Zn is principal?

    I've proved that if K is an ideal of Zn that contains an element k then it contains all the elements of the form mk (m in Zn)...But how can I prove that there are no elements that are not of the form mk?


    THanks!
    HINT: Look at what Euclid's algorithm tells you (that is, look at Bézout's identity).
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