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Prove the set of integers is a commutative ring with identity

  1. Nov 10, 2012 #1
    How should one prove that the integers form a commutative ring? Im not sure exactly where to go with this and how much should be explicitly shown.

    A ring is meant to be a system that shares properties of Z and Zn. A commutative ring is a ring, with the commutative multiplication property. Only need to prove then that that the integers have a commutative multiplication property in that case?? But commutativity of multiplication is a known property of the set of integers, "an arithmetical fact" as my book says. So do I just cite this fact/theorem without having to show much algebra bingo bango its a com. ring? Same argument witht the identity elemnt. It is part of the list of arithmetic facts given to us, which themselves are not proven, so just cite it?
     
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  3. Nov 10, 2012 #2

    micromass

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    We can't answer this. You need to ask your professor whether you can just cite these facts without explicitly showing them.
     
  4. Nov 10, 2012 #3
    I had that feeling haha. Thanks.
     
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