Theorems · Theorem · ring theory
Algebra.linearMap_apply
∀ (R : Type u) (A : Type w) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (r : R), (Algebra.linearMap R A) r = (algebraMap R A) r
- Defined in
- Mathlib.Algebra.Algebra.Defs
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
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 · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- Algebra.linearMapstatement · cited by 157
Cited by12
Results whose statement or proof uses this declaration.
- FractionalIdeal.exists_eq_spanSingleton_mulproof · cited by 6
- not_dvd_differentIdeal_of_intTrace_not_memproof · cited by 1
- IsLocalization.mem_span_mapproof · cited by 1
- RootPairing.algebraMap_root'In_applyproof · cited by 1
- NumberField.exists_ideal_in_class_of_norm_leproof · cited by 1
- PolynomialModule.aeval_equivPolynomialproof · cited by 1
- IsLocalization.smul_mem_finsetIntegerMultiple_spanproof · cited by 1
- Module.Basis.ofIsLocalizedModule_repr_applyproof · cited by 1
- FractionalIdeal.extended_coeIdeal_eq_mapproof · cited by 1
- TensorAlgebra.ι_range_disjoint_oneproof · cited by 0
- FractionalIdeal.extended_oneproof · cited by 0
- FractionalIdeal.div_oneproof · cited by 0