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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.

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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.

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