I'm taking an independent study class over Groups. Rings, and Fields. It's been really confusing. On one page I understand everything completly and the next page I'm completly lost. I'm looking at a problem where I has to show that {x+y(cuberoot of 3) + z(cuberoot of 9) | x,y,z is in Q} is a subring. Now I think I got that...but then I want to prove that it's a subfield. Since I prove that it's a non-empty subset and closed under addition and multiplication by showing that it's a subring, then all I further have to show is that it's a field. (Because to show something is a subfield you just have to show that it's a subset and a field.)(adsbygoogle = window.adsbygoogle || []).push({});

Then to show that the ring is a field you just have to prove it's closed under addition, subtraction, multiplication, division, and it must be cummutative....Right??? So in this case I just have to prove that it's closed under division and cummutative??

I know that my denominator will look like: x^3 + 3y^3 +9z^3 - 9xyz but I really need help!!

Thanks!!

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# Subrings and Subfields

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