Theorems · Theorem · commutative algebra
PowerBasis.coe_basis
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : Algebra R S] (pb : PowerBasis R S),
⇑pb.basis = fun i => pb.gen ^ ↑i- Defined in
- Mathlib.RingTheory.PowerBasis
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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 · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Module.Basisstatement · cited by 1,477
- PowerBasis.genstatement · cited by 122
- PowerBasisstatement and proof · cited by 115
- PowerBasis.dimstatement · cited by 74
- PowerBasis.basisstatement · cited by 54
- PowerBasis.basis_eq_powproof · cited by 13
Cited by12
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.discr_prime_powproof · cited by 3
- PowerBasis.aeval_minpolyGenproof · cited by 3
- IsCyclotomicExtension.Rat.discr_prime_powproof · cited by 2
- Algebra.embeddingsMatrixReindex_eq_vandermondeproof · cited by 2
- PowerBasis.exists_smodEqproof · cited by 1
- PowerBasis.repr_mul_isIntegralproof · cited by 1
- IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_pow_ne_twoproof · cited by 1
- PowerBasis.toMatrix_isIntegralproof · cited by 1
- Algebra.discr_mul_isIntegral_mem_adjoinproof · cited by 1
- Module.Basis.traceDual_powerBasis_eqproof · cited by 1
- PowerBasis.exists_eq_aevalproof · cited by 1
- IsCyclotomicExtension.discr_prime_pow_ne_two'proof · cited by 0