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Math Help - Subring?

  1. #1
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    Subring?

    Ok.

    End of semester is up and my professor is pounding new information down our throats in an effort to exhaust the outlined curriculum. We've barely covered definitions of rings, subrings, ideals, etc. We've got our final homework problems and I'm struggling on a couple.

    For one problem, I'm supposed to determine whether or not a set is a subring.

    Decide whether or not R is a subring of S where R is the set of all rational numbers of the form a/1 and S = rational numbers.

    I want to say yes to this, because to be a subring it must be closed under multiplication and addition and needs 1. It has 1 (duh). To be closed, 1 needs to be multiplicatively closed. My gut tells me it is a subring, but this is a multi part question and all the other answers are "yes it is a subring" and I was fairly certain about those answers until everything started looking like 'yes'. ahhh. Why ask "are they" if they all are?

    Please help clear the fog.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by kpizle View Post
    Ok.

    End of semester is up and my professor is pounding new information down our throats in an effort to exhaust the outlined curriculum. We've barely covered definitions of rings, subrings, ideals, etc. We've got our final homework problems and I'm struggling on a couple.

    For one problem, I'm supposed to determine whether or not a set is a subring.

    Decide whether or not R is a subring of S where R is the set of all rational numbers of the form a/1 and S = rational numbers.

    I want to say yes to this, because to be a subring it must be closed under multiplication and addition and needs 1. It has 1 (duh). To be closed, 1 needs to be multiplicatively closed. My gut tells me it is a subring, but this is a multi part question and all the other answers are "yes it is a subring" and I was fairly certain about those answers until everything started looking like 'yes'. ahhh. Why ask "are they" if they all are?

    Please help clear the fog.
    Yes, this is a subring. It is isomorphic to the integers ( \phi: \frac{a}{1} \mapsto a).

    Perhaps you answered one of the other problems incorrectly? Alternatively, they are all subrings, and your lecturer is just trying to catch people out.
    Last edited by Swlabr; December 10th 2009 at 01:40 AM.
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  3. #3
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    Quote Originally Posted by Swlabr View Post
    Yes, this is a subring. It is isomorphic to the integers ( \phi: \frac{a}{1} \mapsto a).

    Perhaps you answered one of the other problems incorrectly? Alternatively, they are all subrings, and your lecturer is just trying to catch people out.
    Thank you very much!

    I think you are right about my prof trying to catch people. I have been able to justify the others are subrings for sure (I hope ). I'm pretty confidant...

    Thanks again!
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