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Math Help - Rings

  1. #1
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    Rings

    Example of Subring is commutative whereas whole ring is not commutative??
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  2. #2
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    Re: Rings

    help me out plllllllllll
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  3. #3
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    Re: Rings

    sure.

    let R = the ring of all 2x2 matrices with integer entries. this is clearly a non-commutative ring (for example, the matrices:

    A = \begin{bmatrix}1&0\\1&0 \end{bmatrix};\ B = \begin{bmatrix}1&1\\0&0 \end{bmatrix}

    do not commute).

    but the matrices of the form:

    K = \begin{bmatrix}k&0\\0&k \end{bmatrix},\ k \in \mathbb{Z}

    form a sub-ring of R isomorphic to the integers, which is thus commutative.
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  4. #4
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    Re: Rings

    thank u sooooooo muchhhhhhhhh
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