Theorems · Theorem · commutative algebra
Algebra.lmul_algebraMap
∀ (R : Type u) {A : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (x : R),
(Algebra.lmul R A) ((algebraMap R A) x) = (Algebra.lsmul R R A) x- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Tower
- Cited by
- 2 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- AlgHomstatement · cited by 3,236
- LinearMap.extproof · cited by 844
- Module.Endstatement · cited by 774
- Algebra.smul_defproof · cited by 287
- Algebra.lmulstatement · cited by 41
- Algebra.lsmulstatement · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.norm_algebraMapproof · cited by 13
- Algebra.norm_algebraMap_of_basisproof · cited by 3