Theorems · Theorem · commutative algebra
smul_mem_of_normal
Deprecated since 2026-05-28Use IsGaloisGroup.smul_mem_of_normal instead.
∀ (G : Type u_1) (B : Type u_3) [inst : Group G] [inst_1 : Semiring B] [inst_2 : MulSemiringAction G B] {C : Type u_4}
[inst_3 : CommSemiring C] [inst_4 : Algebra C B] (N : Subgroup G) [hN : N.Normal] [hC : IsGaloisGroup (↥N) C B]
(g : G) (x : C), g • (algebraMap C B) x ∈ Set.range ⇑(algebraMap C B)Alias of IsGaloisGroup.smul_mem_of_normal.
- Defined in
- Mathlib.RingTheory.IsGaloisGroup.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Semiringstatement · cited by 13,802
- Algebrastatement · cited by 11,388
- CommSemiringstatement · cited by 10,911
- RingHomstatement · cited by 10,189
- Groupstatement · cited by 6,238
- Algebra.algebraMapstatement · cited by 4,706
- Set.rangestatement · cited by 4,705
- Subgroupstatement · cited by 3,593
- MulSemiringActionstatement · cited by 423
- Subgroup.Normalstatement · cited by 334
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