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Math Help - Algebra....subrings

  1. #1
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    Unhappy Algebra....subrings

    Give an example of a ring R and a subring S of R so that R and S both have an
    identity but 1S is not equal to 1R.


    Any idea? I've spent almost an hour to do this, but still haven't got the answer.
    The midterm is coming soon, hope someone can help me to solve this problem.

    Thanks x 1000
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  2. #2
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    Quote Originally Posted by suedenation
    Give an example of a ring R and a subring S of R so that R and S both have an
    identity but 1S is not equal to 1R.


    Any idea? I've spent almost an hour to do this, but still haven't got the answer.
    The midterm is coming soon, hope someone can help me to solve this problem.

    Thanks x 1000
    If I understand 1S and 1R as cosests. Then since 1 is identity, 1S=S and 1R=R. Thus, the problem reduces to finding a PROPER subring of a ring.
    Take any ring <\mathcal{R},+,\cdot> then the trivial subring \{0\} satisfies these conditions.
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