Theorems · Theorem · ring theory
RingHom.algebraMap_toAlgebra
∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring S] (i : R →+* S), algebraMap R S = i- Defined in
- Mathlib.Algebra.Algebra.Defs
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses no axioms
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- RingHom.toAlgebrastatement · cited by 337
Cited by31
Results whose statement or proof uses this declaration.
- isCusp_SL2Z_iff'proof · cited by 7
- RingHom.FaithfullyFlat.iff_flat_and_comap_surjectiveproof · cited by 5
- isCusp_SL2Z_iffproof · cited by 3
- Algebra.trace_quotient_eq_of_isDedekindDomainproof · cited by 3
- Ideal.spanIntNorm_localizationproof · cited by 3
- AlgebraicGeometry.isLocalization_basicOpen_of_qcqsproof · cited by 3
- IsLocalization.isLocalization_iff_of_base_ringEquivproof · cited by 2
- AlgebraicGeometry.HasRingHomProperty.of_source_openCoverproof · cited by 2
- AlgebraicGeometry.IsAffineOpen.appLE_eq_away_mapproof · cited by 2
- AlgebraicGeometry.IsAffineOpen.basicOpen_basicOpen_is_basicOpenproof · cited by 2
- HomogeneousLocalization.Away.isLocalization_mulproof · cited by 2
- LinearMap.transvection.detproof · cited by 1