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Thread: Artinian Modules - Cohn Exercise 3, Section 2.2, page 65

  1. Nov 9, 2015 #1
    I am reading P.M. Cohn's book: Introduction to Ring Theory (Springer Undergraduate Mathematics Series) ... ...

    I am currently focused on Section 2.2: Chain Conditions ... which deals with Artinian and Noetherian rings and modules ... ...

    I need help to get started on Exercise 3, Section 2.2, page 65 ...

    Exercise 3 (Section 2.2, page 65) reads as follows:



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    Any help will be much appreciated ...

    Peter
     

    Attached Files:

  2. jcsd
  3. Nov 10, 2015 #2

    fresh_42

    Staff: Mentor

    The same exercise is in my book (see your other thread). There Atiyah, Macdonald give the following hints:
    Let ##φ : M → M## be the endomorphism. To prove the Noetherian case consider the submodules ##ker(φ^n)## and in the Artian case the quotient modules ##coker(φ^n) = M / im(φ^n) , n ∈ℕ.##
     
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