(adsbygoogle = window.adsbygoogle || []).push({});

I'll skip out some tedious bits that I'm confident I have correct and get to the part I'm stuck on

Let L = Q(3^{1/3})

[L:Q] = 3

Clearly [K:L] >1

w is a root of X^{3}-1

So

[K:L] is less than or equal to 3, in particular it is either 2 or 3

Here is where i'm stuck

I tried to show that X^{3}-1 is the min poly of K over L by supposing there exists an a,b in Q such that

(a+b(3^{1/3})) = 1

with a hope of finding a contradiction, but when a=1 this is clearly a root and 1 is an element of L, so this canot be the minimal polynomial of K over L.

Can anyone help me find the minimal polynomial of K over L?

Thanks

Matt

**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!

# Compute the degree of K over Q

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