(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let F = {a + b[itex]\sqrt[3]{2}[/itex]:a,b[itex]\in[/itex]Q}.

Using the fact that [itex]\sqrt[3]{2}[/itex] is irrational, show that F is not a field.

[Hint: What is the inverse of [itex]\sqrt[3]{2}[/itex] under multiplication?]

2. Relevant equations

For a field,

For all c [itex]\in[/itex] F, there exists c^{-1}[itex]\in[/itex] F s.t. c*c^{-1}=1

3. The attempt at a solution

I am unsure how to relate the axioms to the set. Is c = (a +b[itex]\sqrt[3]{2}[/itex])?

Or show there is no b[itex]\sqrt[3]{2}[/itex]*b^{-1}[itex]\sqrt[3]{2}[/itex]=1?

Or b[itex]\sqrt[3]{2}[/itex]*(b[itex]\sqrt[3]{2}[/itex])^{-1}=1?

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# Homework Help: Using field axioms to prove a set is not a field

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