Find the ring of algebraic integers.

Asked Oct 18 '14 at 19:53

Active Oct 18 '14 at 20:01

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Find the ring of algebraic integers in $K=\mathbb Q(\sqrt[3]{2})$.

So, I know that $K=\{a+b\sqrt[3]{2}+c\sqrt[3]{2}^2 \mid a,b,c \in \mathbb Q\}$.

My professor has done very little on this topic. I know that an algebraic integer is the root of a monic polynomial with integer coefficients.

I have no clue on where to start with this question. Any help is much appreciated!

edited Oct 18 '14 at 20:01

Thomas Andrews

asked Oct 18 '14 at 19:53

NL37

A good guess is to try $\mathbb{Z}[\sqrt[3]{2}]$. There depending of how much algberaic number theory you know will be easier or harder to prove. – Josué Tonelli-Cueto Oct 18 '14 at 20:04
1

See if this post helps. – Aaron Maroja Oct 18 '14 at 20:09
Are you familiar with the trace function? – Jyrki Lahtonen Oct 18 '14 at 21:47

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