Theorems · Theorem · ring theory
Subalgebra.mem_map
∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : Semiring B] [inst_4 : Algebra R B] {S : Subalgebra R A} {f : A →ₐ[R] B} {y : B},
y ∈ Subalgebra.map f S ↔ ∃ x ∈ S, f x = y- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- AlgHomstatement and proof · cited by 3,236
- Subalgebrastatement and proof · cited by 1,353
- Subalgebra.mapstatement · cited by 90
- Subsemiring.mem_mapproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.isGaloisproof · cited by 13
- Subalgebra.comap_map_eqproof · cited by 1
- integralClosure_map_algEquivproof · cited by 0