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Math Help - Noetherian problem

  1. #1
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    Noetherian problem

    a. A commutative ring R is said to be noetherian if every increasing chain, I1 I2⊆ ... In⊆ ... , of ideals stabilizes.
    If R is Noetherian show that any surjective ring endomorphism f:R --> R is an isomorphism.

    b. Is Z Noetherian? Why or why not?
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  2. #2
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    Re: Noetherian problem

    Hi,
    Here's a solution to your first question. I left to you to figure out a proof that Z is Noetherian.

    Noetherian problem-mhfrings2.png
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