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Math Help - need more examples about ring -_-?

  1. #1
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    Red face need more examples about ring -_-?

    Please give me EXAMPLE and explain about:

    - Commutative ring and uncommutative ring which doesn't have unit element
    - Ring which has different unit element with its subring's unit element

    thank you
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  2. #2
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    Quote Originally Posted by GTK X Hunter View Post
    Please give me EXAMPLE and explain about:

    - Commutative ring and uncommutative ring which doesn't have unit element
    n\mathbb{Z}, \ n > 1, for the commutative case and \left \{ \begin{pmatrix} a & b \\ 0 & 0 \end{pmatrix}: \ a,b \in \mathbb{R} \right \} for the noncommutative case.

    - Ring which has different unit element with its subring's unit element

    thank you
    M_2(\mathbb{R}) and the subring \left \{\begin{pmatrix}a & 0 \\ 0 & 0 \end{pmatrix}: \ a \in \mathbb{R} \right \}.
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