Abstract Algebra: Theory and Applications · Problem 22.4.5

Galois Theory — Thomas Judson

Mathematics — Abstract Algebra · finite-fields-construction

Problem

Construct a finite field of order 27. Hint. Find an irreducible polynomial p(x)p(x) in Z3[x]\mathbb{Z}_3[x] of degree 3 and show that Z3[x]/⟨p(x)⟩\mathbb{Z}_3[x]/\langle p(x) \rangle has 27 elements.

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