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Math Help - Ideals of ring of square matrices having rational entries...

  1. #1
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    Bhubaneswar
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    Ideals of ring of square matrices having rational entries...

    set of all 2*2 matrices forms a ring

    I want to prove that its only Ideals are Zero matrix and ring itself.

    How to prove it??

    Thank you in advance
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  2. #2
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    Quote Originally Posted by greatharish View Post
    set of all 2*2 matrices forms a ring

    I want to prove that its only Ideals are Zero matrix and ring itself.

    How to prove it??

    Thank you in advance
    More generally, every two sided ideal of matrix ring M_n(R) is equal to M_n(I) for some two-sided ideal I of R. Since Q is a field, its ideals are (0) and Q itself. Now the conclusion follows.
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