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Math Help - ideal problem....

  1. #1
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    ideal problem....

    Q:A ring R has maximum ideals
    a)if R is infinite
    b)if R is finite
    c)if R is finite atleast 2 elements
    d)only if R is finite
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  2. #2
    Super Member Gamma's Avatar
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    Not sure I understand

    Is only one allowed to be true? I havent thought about the others, and I cannot be positive that all infinite rings posses maximum ideals, but certainly the following does.


    Consider a polynomial ring with coefficients from a field \mathbb{F}. \mathbb{F}[x] is an infinite ring a Principal Ideal Domain and any irreducible polynomial forms a maximal ideal since in PIDs irreducible implies prime which implies maximal.
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  3. #3
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    Quote Originally Posted by Mathventure View Post

    Q:A ring R has maximum ideals

    a) if R is infinite

    b) if R is finite

    c) if R is finite at least 2 elements

    d) only if R is finite
    c) is the answer. (no more explaining from me! that kind of asking question deserves this kind of answer!)
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