Theorems · Theorem · commutative algebra
Algebra.IsAlgebraic.rank_fractionRing_mvPolynomial
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[alg : Algebra.IsAlgebraic R S] [inst_3 : IsDomain S] [inst_4 : FaithfulSMul R S] (σ : Type u),
Module.rank (FractionRing (MvPolynomial σ R)) (FractionRing (MvPolynomial σ S)) =
Cardinal.lift.{u, u_2} (Module.rank R S)[Stacks Tag 0G1M](https://stacks.math.columbia.edu/tag/0G1M)
- Defined in
- Mathlib.RingTheory.Algebraic.Integral
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
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- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- 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
- nonZeroDivisorsstatement · cited by 895
- Cardinal.liftstatement and proof · cited by 583
- Module.rankstatement and proof · cited by 496
- FaithfulSMulstatement and proof · cited by 340
- Algebra.IsAlgebraicstatement and proof · cited by 322
- FractionRingstatement · cited by 200
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