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Math Help - Unity in a Subring

  1. #1
    Senior Member slevvio's Avatar
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    Unity in a Subring

    Hello everyone. I was wondering if anyone could think of an example of a subring of a commutative ring (with unity), that does not have the same unity?
    I can think of one with a non-commutative ring:

     \left\{ \left( \begin{array}{cc} x & 0 \\ 0 & 0 \\ \end{array} \right) } \mid x \in \mathbb{R} \right\} which has a different unity element from M_2(\mathbb{R}).

    Thanks for any help
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  2. #2
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    Quote Originally Posted by slevvio View Post
    Hello everyone. I was wondering if anyone could think of an example of a subring of a commutative ring (with unity), that does not have the same unity?
    I can think of one with a non-commutative ring:

     \left\{ \left( \begin{array}{cc} x & 0 \\ 0 & 0 \\ \end{array} \right) } \mid x \in \mathbb{R} \right\} which has a different unity element from M_2(\mathbb{R}).

    Thanks for any help
    \mathbb{Z} as a subring of \mathbb{Z} \oplus \mathbb{Z}.
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  3. #3
    Senior Member slevvio's Avatar
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    thanks!
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