Theorems · Theorem · commutative algebra
PowerBasis.basis_eq_pow
∀ {R : Type u_7} {S : Type u_8} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : Algebra R S] (self : PowerBasis R S)
(i : Fin self.dim), self.basis i = self.gen ^ ↑i- Defined in
- Mathlib.RingTheory.PowerBasis
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
Cited by13
Results whose statement or proof uses this declaration.
- PowerBasis.coe_basisproof · cited by 12
- PowerBasis.constr_pow_aevalproof · cited by 4
- PowerBasis.adjoin_gen_eq_topproof · cited by 4
- WeierstrassCurve.Affine.CoordinateRing.basis_applyproof · cited by 2
- IsCyclotomicExtension.Rat.discr_prime_powproof · cited by 2
- PowerBasis.repr_gen_pow_isIntegralproof · cited by 2
- PowerBasis.dim_le_natDegree_of_rootproof · cited by 1
- IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_pow_ne_twoproof · cited by 1
- PowerBasis.repr_pow_isIntegralproof · cited by 1
- traceForm_dualSubmodule_adjoinproof · cited by 1
- Algebra.discr_mul_isIntegral_mem_adjoinproof · cited by 1
- PowerBasis.leftMulMatrixproof · cited by 0