Theorems · Theorem · commutative algebra
IsGaloisGroup.faithful
∀ {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} [self : IsGaloisGroup G A B], FaithfulSMul G B- Defined in
- Mathlib.RingTheory.IsGaloisGroup.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- IsGaloisGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Groupstatement and proof · cited by 6,238
- MulSemiringActionstatement and proof · cited by 423
- FaithfulSMulstatement · cited by 340
- IsGaloisGroupstatement and proof · cited by 96
Cited by6
Results whose statement or proof uses this declaration.
- IsGaloisGroup.card_eq_finrankproof · cited by 10
- IsGaloisGroup.of_isFractionRingproof · cited by 5
- IsGaloisGroup.to_isFractionRing_of_isIntegralproof · cited by 2
- IsGaloisGroup.of_ringHom_surjectiveproof · cited by 1
- IsGaloisGroup.map_quotientMk'proof · cited by 1
- IsGaloisGroup.fixingSubgroup_topproof · cited by 0