Theorems · Theorem · ring theory
DistribSMul.toLinearMap_apply
∀ (R : Type u_1) {S : Type u_3} (M : Type u_4) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : DistribSMul S M] [inst_4 : SMulCommClass S R M] (s : S) (a : M), (DistribSMul.toLinearMap R M s) a = s • a- Defined in
- Mathlib.Algebra.Module.LinearMap.End
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses no axioms
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- SMulCommClassstatement and proof · cited by 1,927
- DistribSMulstatement and proof · cited by 117
- DistribSMul.toLinearMapstatement and proof · cited by 50
Cited by18
Results whose statement or proof uses this declaration.
- Polynomial.hasseDeriv_applyproof · cited by 6
- FractionalIdeal.equivNum_applyproof · cited by 1
- LinearEquiv.mem_stabilizer_submodule_of_le_fixedSubmoduleproof · cited by 1
- toMatrix_distrib_mul_action_toLinearMapproof · cited by 1
- Real.doublingGamma_log_convex_Ioiproof · cited by 1
- AddSubgroup.distribSMulToLinearMap_injective_of_isTorsionFreeproof · cited by 1
- Submodule.mem_smul_iff_inv_mul_memproof · cited by 1
- AddSubgroup.finrank_eq_of_finiteIndexproof · cited by 1
- IsLocalization.Away.of_surjectiveproof · cited by 1
- Module.End.span_orbit_mem_invtSubmoduleproof · cited by 1
- LieAlgebra.ad_isSemisimple_of_isSemisimpleproof · cited by 1
- Submodule.set_smul_eq_mapproof · cited by 1