Theorems · Theorem · ring theory
Algebra.lmul_injective
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A],
Function.Injective ⇑(Algebra.lmul R A)- Defined in
- Mathlib.Algebra.Algebra.Bilinear
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- mul_oneproof · cited by 3,885
- AlgHomstatement · cited by 3,236
- Module.Endstatement · cited by 774
- DFunLike.congr_funproof · cited by 288
- Algebra.lmulstatement and proof · cited by 41
- LinearMap.mul_apply_applyproof · cited by 25
Cited by5
Results whose statement or proof uses this declaration.
- IsIntegral.of_finiteproof · cited by 16
- isNilpotent_tensor_residueField_iffproof · cited by 1
- minpoly.natDegree_le_spanFinrankproof · cited by 1
- Module.Free.bijective_algebraMap_of_finrank_eq_oneproof · cited by 1
- Algebra.aeval_self_charpoly_lmulproof · cited by 0