Theorems · Definition · ring theory
AlgHom.codRestrict
{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] → (f : A →ₐ[R] B) → (S : Subalgebra R B) → (∀ (x : A), f x ∈ S) → A →ₐ[R] ↥SRestrict the codomain of an algebra homomorphism.
- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- RingHomproof · cited by 10,189
- AlgHomstatement and proof · cited by 3,236
- Subalgebrastatement and proof · cited by 1,353
- RingHomClass.toRingHomproof · cited by 746
- RingHom.codRestrictproof · cited by 12
Cited by29
Results whose statement or proof uses this declaration.
- AlgHom.rangeRestrictproof · cited by 16
- galRestrict'proof · cited by 7
- TensorProduct.toIntegralClosureproof · cited by 6
- AlgHom.val_comp_codRestrictstatement · cited by 5
- MvPolynomial.renameSymmetricSubalgebraproof · cited by 5
- StarAlgHom.codRestrictproof · cited by 4
- RingCon.quotientKerEquivRangeₐproof · cited by 4
- AlgHom.subalgebraMapproof · cited by 3
- algebraMap_galRestrict'_applyproof · cited by 3
- IntermediateField.algHomEquivAlgHomOfSplitsproof · cited by 3
- Field.nonempty_algHom_of_exists_rootproof · cited by 3
- PolynomialLaw.isCompat_applyproof · cited by 2