Theorems · Theorem · field theory
MvPolynomial.trdeg_of_isDomain
∀ {ι : Type u} {S : Type v} [inst : CommRing S] [IsDomain S],
Algebra.trdeg S (MvPolynomial ι S) = Cardinal.lift.{v, u} (Cardinal.mk ι)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Finsuppstatement · cited by 5,255
- Cardinalstatement and proof · cited by 2,598
- IsDomainstatement and proof · cited by 2,196
- MvPolynomialstatement and proof · cited by 2,140
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- Cardinal.lift_idproof · cited by 163
- Cardinal.lift_liftproof · cited by 53
- Cardinal.lift_id'proof · cited by 43
- Algebra.trdegstatement and proof · cited by 39
- IsTranscendenceBasis.lift_cardinalMk_eq_trdegproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- trdeg_lt_aleph0_of_finiteTypeproof · cited by 1