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Math Help - Affine varieties

  1. #1
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    Affine varieties

    (1) An integral domain A is a principal ideal domain if every ideal I of A is principal, that is of the form I = (a); show directly that the ideals in a PID satisfy the a.c.c. (ascending chain condition).

    (2) Show that an integral domain A is a UFD if and only if every ascending chain of principal ideals terminates, and every irreducible element of A is prime

    No idea! Any help would be appreciated, thanks!
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  2. #2
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    Quote Originally Posted by shadow_2145 View Post
    (1) An integral domain A is a principal ideal domain if every ideal I of A is principal, that is of the form I = (a); show directly that the ideals in a PID satisfy the a.c.c. (ascending chain condition).

    (2) Show that an integral domain A is a UFD if and only if every ascending chain of principal ideals terminates, and every irreducible element of A is prime

    No idea! Any help would be appreciated, thanks!
    you'll find complete and easy to understand solution to your problem in here.
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