ma103bhw3solns

Ma103bhw3solns

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Unformatted text preview: So fg = 0 function. The rationals are a field as stated in a). Define g to be non-0 at x0 but 0 everywhere else. Then fg=0. and 6 is the smallest n such that n.a=0. If a and b are in F*, then ab can't be 0 as F has no zero divisors so ab is in F*. Also 1 is not equal to 0 so it must be in F*. This means F* is closed under multiplication and has an identity for multiplication. If a is not 0, then a-1 is not 0, as aa-1=1. Thus every element of F* has an inverse. So F* is a group under multiplication, as we know multiplication is associative in a field....
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