Theorems · Theorem · commutative algebra
PowerBasis.finrank
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : Ring S] [inst_2 : Algebra R S] [StrongRankCondition R]
(pb : PowerBasis R S), Module.finrank R S = pb.dim- Defined in
- Mathlib.RingTheory.PowerBasis
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 114 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Module.finrankstatement · cited by 1,770
- StrongRankConditionstatement and proof · cited by 286
- Fintype.card_finproof · cited by 270
- PowerBasisstatement and proof · cited by 115
- PowerBasis.dimstatement and proof · cited by 74
- PowerBasis.basisproof · cited by 54
- Module.finrank_eq_card_basisproof · cited by 40
Cited by14
Results whose statement or proof uses this declaration.
- IntermediateField.adjoin.finrankproof · cited by 14
- IsCyclotomicExtension.finrankproof · cited by 12
- X_pow_sub_C_irreducible_of_primeproof · cited by 2
- IsCyclotomicExtension.Rat.discr_prime_powproof · cited by 2
- IsAdjoinRootMonic.finrankproof · cited by 2
- finrank_quotient_span_eq_natDegreeproof · cited by 2
- dvd_coeff_zero_of_aeval_eq_prime_smul_of_minpoly_isEisensteinAtproof · cited by 1
- det_traceMatrix_ne_zero'proof · cited by 1
- AlgHom.natCard_of_splitsproof · cited by 1
- mem_adjoin_of_smul_prime_smul_of_minpoly_isEisensteinAtproof · cited by 1
- finrank_quotient_span_eq_natDegree_normproof · cited by 1
- Algebra.discr_powerBasis_eq_normproof · cited by 1