# F[x]/(f(x)) is a field with p^n elements.

Modern Algebra

Ring Theory (XXXII)

Polynomial Ring

Irreducible Polynomial

If f(x) is in F[x], where F is the field of integers mod p, p a prime, and f(x) is irreducible over F of degree n,

prove that F[x]/(f(x)) is a field with p^n elements.

#### Solution Preview

See the attached file for the solution of the problem.

Modern Algebra

Ring Theory (XXXII)

Polynomial Ring

Irreducible Polynomial

By:- Thokchom Sarojkumar Sinha

If is in , where is the field of integers mod , a prime , and is irreducible over of ...

#### Solution Summary

It id the explanation of the following topic:

If f(x) is in F[x], where F is the field of integers mod p, p a prime, and f(x) is irreducible over F of degree n, then F[x]/(f(x)) is a field with p^n elements.

The solution is given in detail.