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Math Help - Rings and Ideal

  1. #1
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    Rings and Ideal

    Help me in

    Q1 : give an example of not commutative ring and did not have identity.

    Q2: Suppose R is ring and I_{1},I_{2}are Ideals in R such that : I_{1}\bigcap I_{2}=\{0\}
    Prove is: R=I_{1}\bigoplus I_{2}
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  2. #2
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    Quote Originally Posted by nice rose View Post
    Help me in

    Q1 : give an example of not commutative ring and did not have identity.


    The set of all polynomials over the integer numbers with even free coefficient, wrt the usual operations of sum and multiplication of polynomials.



    Q2: Suppose R is ring and I_{1},I_{2}are Ideals in R such that : I_{1}\bigcap I_{2}=\{0\}
    Prove is: R=I_{1}\bigoplus I_{2}

    As stated the problem is false big time: just take I_1:=\{0\}= the zero ideal to get a contradiction, with R any nonzero ring and I_2 any non-trivial proper ideal.

    Check carefully the conditions...

    Tonio



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