- #1
Firepanda
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For i) I said for a in [0,1], then the group of units are = {f in R | f(a) =/= 0}
i.e a continuous function f on [0,1] would have a continuous function g on [0,1] such that f.g=1
but the function would have to be g = 1/f, but this wouldn't be continuous if f(a) = 0
for ii) I have to show for a,b in R then if ab=0 then either a = 0 or b = 0
but I havn't gotton any further here since I'm having a hard time finding functions a and b where the product is 0
for iii) I believe I have to construct a surjective ring homomorphism ( f: R -> F ) and show that the kernal is equal to the Ideal.
But I'm not sure how what field F to choose for this
Or I have to show that the quotient group R/I is a field.
Thanks for any help!
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