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Finite Fields

Definition

Associate

Theorem

Characteristic of F

Theorem

Degree is Closed under Addition

Theorem

Division Algorithm for Polynomials

Theorem

Division of Polynomials

Theorem

Finite Fields of Same Cardinality = Isomorphic

Theorem

Finite Subgroups are Cyclic

Theorem

Gauss's Formula

Definition

Generator

Theorem

If an Irreducible Polynomial divides ab then it divides a or b

Definition

Irreducible (Polynomial)

Theorem

Irreducible Factorization

Theorem

Lagrange Corollary

Theorem

Lagrange Lemma

Theorem

Lagrange Theorem

Theorem

lcm Order Lemma

Theorem

Min poly. dividing poly. of same root

Definition

Minimal Polynomial

Definition

Monic

Definition

Nonzero Constant Polynomials

Definition

Polynomials

Definition

Primitive Root

Definition

Relatively Prime

Definition

Ring of Polynomials of Order p

Definition

Root

Definition

Root of Unity

Theorem

Unique Factorization Theorem for Polynomials

Theorem

Uniqueness of GCD

Theorem

Wilson's Theorem