OurBigBook About$ Donate
 Sign in+ Sign up
by Ciro Santilli (@cirosantilli, 37)

Finite field of non-prime order

 ... Area of mathematics Algebra Group Ring (mathematics) Field (mathematics) Finite field
 0 By others on same topic  0 Discussions  Updated 2025-05-26  +Created 1970-01-01  See my version
As per classification of finite fields those must be of prime power order.
Video "Finite fields made easy by Randell Heyman (2015)" at youtu.be/z9bTzjy4SCg?t=159 shows how for order 9=3×3. Basically, for order pn, we take:
  • each element is a polynomial in GF(p)[x], GF(p)[x], the polynomial ring over the finite field GF(p) with degree smaller than n. We've just seen how to construct GF(p) for prime p above, so we're good there.
  • addition works element-wise modulo on GF(p)
  • multiplication is done modulo an irreducible polynomial of order n
For a worked out example, see: GF(4).

 Ancestors (8)

  1. Finite field
  2. Field (mathematics)
  3. Ring (mathematics)
  4. Group
  5. Algebra
  6. Area of mathematics
  7. Mathematics
  8.  Home

 Incoming links (2)

  • Finite field
  • GF(4)

 View article source

 Discussion (0)

+ New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.
  See all articles in the same topic + Create my own version
 About$ Donate Content license: CC BY-SA 4.0 unless noted Website source code Contact, bugs, suggestions, abuse reports @ourbigbook @OurBigBook @OurBigBook