Theorems · Theorem · field theory
AlgebraicIndependent.matroid_cRank_eq
∀ (R : Type u_1) (A : Type w) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] [inst_3 : FaithfulSMul R A] [inst_4 : NoZeroDivisors A], (AlgebraicIndependent.matroid R A).cRank = Algebra.trdeg R A
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 145 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Cardinalstatement · cited by 2,598
- NoZeroDivisorsstatement and proof · cited by 545
- FaithfulSMulstatement and proof · cited by 340
- Algebra.trdegstatement · cited by 39
- AlgebraicIndependent.matroidstatement · cited by 17
- Matroid.cRankstatement · cited by 17
- trdeg_eq_iSup_cardinalMk_isTranscendenceBasisproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- IsTranscendenceBasis.lift_cardinalMk_eq_trdegproof · cited by 7
- Algebra.IsAlgebraic.isTranscendenceBasis_of_lift_le_trdeg_of_finiteproof · cited by 2
- AlgebraicIndependent.isTranscendenceBasis_of_lift_trdeg_leproof · cited by 2
- Algebra.IsAlgebraic.trdeg_le_cardinalMkproof · cited by 1