Subfields of $F_2[x] / (x^3 + x + 1)$

Question

What are the subfields of $F_2[x] / (x^3 + x + 1)$? I know $F_2$ is a subfield, and so is itself, but I'm not sure if there are any more.

Thanks!

What is $F_2$? a field with 2 elements? – user 1 Mar 01 '15 at 08:02 — user 1, Mar 01 '15 at 08:02

score 3 · Accepted Answer · edited Apr 13 '17 at 12:20

3

Subfileds of any finite field of order $p^n$ are exactly of order $p^r$ where $r$ divides $n$.You may see it here:Subfields of finite fields. Now can you conclude?

edited Apr 13 '17 at 12:20

Community

1

answered Mar 01 '15 at 04:41

Arpit Kansal

10,268

Subfields of $F_2[x] / (x^3 + x + 1)$

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