Theorems · Theorem · ring theory
LinearMap.mulLeft_apply
∀ (R : Type u_14) {A : Type u_15} [inst : Semiring R] [inst_1 : NonUnitalNonAssocSemiring A] [inst_2 : Module R A]
[inst_3 : SMulCommClass R A A] (a b : A), (LinearMap.mulLeft R a) b = a * b- Defined in
- Mathlib.Algebra.Module.LinearMap.Defs
- Cited by
- 3 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- SMulCommClassstatement and proof · cited by 1,927
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- LinearMap.mulLeftstatement · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- CliffordAlgebra.toEven_ιproof · cited by 3
- JacobsonNoether.exist_pow_eq_zero_of_leproof · cited by 1
- JacobsonNoether.exists_separable_and_not_isCentralproof · cited by 1