Theorems · Theorem · ring theory
Algebra.mul_sub_algebraMap_pow_commutes
∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Ring A] [inst_2 : Algebra R A] (x : A) (r : R)
(n : ℕ), x * (x - (algebraMap R A) r) ^ n = (x - (algebraMap R A) r) ^ n * x- Defined in
- Mathlib.Algebra.Algebra.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
- Assumes
- CommSemiringRingAlgebra
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 and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapstatement and proof · cited by 4,706
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- mul_assocproof · cited by 1,667
- pow_zeroproof · cited by 1,094
- pow_succ'proof · cited by 228
- Algebra.mul_sub_algebraMap_commutesproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Module.End.independent_genEigenspaceproof · cited by 4
- Module.End.map_genEigenrange_leproof · cited by 1