Field F_5 - Knowlpedia

For the field $\mathbb F_5$ is the quotient field $\mathbb Z/5\mathbb Z$ , with residue-class addition and multiplication.

Operations and maps

Every nonzero residue has an inverse because 5 is prime. A unit-preserving field endomorphism fixes $1$ , hence every sum of copies of $1$ , and is therefore the identity. The zero map is allowed as a nonunital ring map, but never as a field map.

Underlying groups

Its additive group is cyclic of order $5$ ; its nonzero elements form a separate multiplicative group of order $5-1$ . These group structures must be selected explicitly before taking group Hom-sets.