Theorems · Definition · commutative algebra

IsGaloisGroup.ringEquivFixedPoints

(G : Type u_1) →
  (A : Type u_2) →
    (B : Type u_4) →
      [inst : Group G] →
        [inst_1 : CommSemiring A] →
          [inst_2 : Semiring B] →
            [inst_3 : Algebra A B] →
              [inst_4 : MulSemiringAction G B] →
                [hA : IsGaloisGroup G A B] → [FaithfulSMul A B] → A ≃+* ↥(FixedPoints.subsemiring B G)

If B/A is Galois with Galois group G, then A is isomorphic to the subring of elements of B fixed by G.

Defined in

Mathlib.RingTheory.IsGaloisGroup.Defs

Cited by

9 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupCommSemiringSemiringAlgebraMulSemiringActionIsGaloisGroupFaithfulSMul