Theorems · Definition · commutative algebra

Fintype.fieldOfDomain

(R : Type u_3) → [inst : CommRing R] → [IsDomain R] → [DecidableEq R] → [Fintype R] → Field R

Every finite commutative domain is a field. More generally, commutativity is not required: this can be found in Mathlib/RingTheory/LittleWedderburn.lean.

Defined in

Mathlib.RingTheory.IntegralDomain

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainDecidableEqFintype