Theorems · Theorem · ring theory
AlgHom.coe_range
∀ {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] (φ : A →ₐ[R] B), ↑φ.range = Set.range ⇑φ- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Set.rangestatement · cited by 4,705
- AlgHomstatement and proof · cited by 3,236
- Subalgebrastatement · cited by 1,353
- AlgHom.rangestatement and proof · cited by 169
Cited by20
Results whose statement or proof uses this declaration.
- Subalgebra.range_valproof · cited by 9
- Algebra.FiniteType.isNoetherianRingproof · cited by 6
- IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singletonproof · cited by 2
- Algebra.adjoin_restrictScalarsproof · cited by 2
- IsScalarTower.adjoin_range_toAlgHomproof · cited by 2
- Algebra.TensorProduct.not_isField_of_transcendentalproof · cited by 1
- polynomialFunctions_coeproof · cited by 1
- Algebra.FiniteType.iff_quotient_freeAlgebraproof · cited by 1
- Algebra.FiniteType.iff_quotient_mvPolynomialproof · cited by 1
- Subalgebra.centralizer_coe_range_includeLeft_eq_center_tensorProductproof · cited by 1
- Subalgebra.centralizer_range_includeRight_eq_center_tensorProductproof · cited by 1