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

I'm doing a question where part of it is to show that the span of the following set over the rationals is a field.

If w is the primitive cube root of unity and z is the positive cube root of 2, the set in question is:

(1,z,z^{2},w, wz, wz^{2})

2. Relevant equations

3. The attempt at a solution

I have already shown this span is closed under multiplication. Almost by definition it is closed under addition/subtraction. I have also shown that each basis element has an inverse in the span. However, when I come to then showing that every element has an inverse, I struggle.. a general element is obviously a linear combination of 6 elements and I can't exactly rationalise the denominator. Any hints at all?

Thanks,

Zoe

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Trying to show a set is a field

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**