I'm trying to find the ideals of $F_2[C_2]$
I believe the elements are $(0,1,x) $
So far I have the ideal {0} I can't seem to spot any others, have I made a mistake or missed something?
2026-04-23 06:31:04.1776925864
Finding ideals of $F_2[C_2]$
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(I'm assuming you are representing the elements of $C_2$ with $\{1,x\}$.)
$C_2$ is a basis for the space, so there are at least $2^2$ elements. You forgot $x+1$, which squares to zero. So $(x+1)$ is another (and the only other) ideal.