Theorems · Theorem · ring theory
AlgEquiv.coe_pow
∀ {R : Type uR} {A₁ : Type uA₁} [inst : CommSemiring R] [inst_1 : Semiring A₁] [inst_2 : Algebra R A₁] (e : A₁ ≃ₐ[R] A₁)
(n : ℕ), ⇑(e ^ n) = (⇑e)^[n]- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
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 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
- AlgEquivstatement and proof · cited by 1,681
- pow_zeroproof · cited by 1,094
- Nat.iteratestatement and proof · cited by 740
- pow_succproof · cited by 374
Cited by7
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.orderOf_complexConjproof · cited by 1
- FiniteField.algebraMap_norm_eq_powproof · cited by 1
- FiniteField.algebraMap_norm_eq_prod_powproof · cited by 1
- NumberField.ComplexEmbedding.orderOf_isConj_two_of_ne_oneproof · cited by 1
- FiniteField.Extension.exists_frob_pow_eqproof · cited by 1
- FiniteField.algebraMap_trace_eq_sum_powproof · cited by 0
- FiniteField.orderOf_frobeniusAlgEquivOfAlgebraicproof · cited by 0