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Math Help - subfield, subrings

  1. #1
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    subfield, subrings

    I have the set K={a+b sqrt(d) with a,b rational} I know how to show it is a subring, but how do I show it is a subfield? I can show a ring is a field, but is the process same to show a subring is a subfield?

    Thanks
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  2. #2
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    Quote Originally Posted by zhupolongjoe View Post
    I have the set K={a+b sqrt(d) with a,b rational} I know how to show it is a subring, but how do I show it is a subfield? I can show a ring is a field, but is the process same to show a subring is a subfield?

    Thanks

    Almost: showing this is a subring and even an integer domain is pretty easy. The tricky thing is to show that any non-zero element has an inverse, but even that is fairly easy. Try it (remember conjugates and stuff).

    Tonio
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