Finite Fields
Copyright policy )Finite Fields
Summary We continue the formalization of field theory in Mizar. Here we prove existence and uniqueness of finite fields by constructing the splitting field of the polynomial X(pn) −X over the prime field of a field with characteristic p. We also define the Frobenius morphism and show that the automorphisms of a field with pn elements are exactly the powers 0, . . ., n − 1 of the Frobenius morphism, that is the automorphism group is generated by the Frobenius morphism.
Galois field, Formalization of mathematics in connection with theorem provers, Finite fields (field-theoretic aspects), splitting field, finite field, 510, 004
Galois field, Formalization of mathematics in connection with theorem provers, Finite fields (field-theoretic aspects), splitting field, finite field, 510, 004
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