Definition talk:Eisenstein Integer

If $\Z \left[{\omega}\right] = \left\{{a + b \omega: a, b \in \Z}\right\}$ then numbers of the form $\left\{{a + b \omega^2: a, b \in \Z}\right\}$ are not in $\Z \left[{\omega}\right]$, or am I missing something? There's something obvious that I'm too tired to get my head round at the moment, I believe ... --prime mover (talk) 23:15, 25 March 2013 (UTC)

$\omega$ is a cube root of $1$ not equal to $1$, so $\omega^2 + \omega + 1 = 0$. Therefore $\omega^2 = -\omega-1 \in \Z \left[{\omega}\right]$, thus the notation is justified. --Linus44 (talk) 23:55, 25 March 2013 (UTC)

Oh yes of course it is. Blame tiredness brought on by overwork. --prime mover (talk) 06:15, 26 March 2013 (UTC)