Theorems · Theorem · commutative algebra
Transcendental.extendScalars
∀ {R : Type u_1} (S : Type u_2) {A : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Ring A]
[inst_3 : Algebra R S] [inst_4 : Algebra R A] [inst_5 : Algebra S A] [IsScalarTower R S A] [NoZeroDivisors S] {a : A},
Transcendental R a → ∀ [Algebra.IsAlgebraic R S], Transcendental S a- Defined in
- Mathlib.RingTheory.Algebraic.Integral
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- IsScalarTowerstatement and proof · cited by 3,896
- NoZeroDivisorsstatement and proof · cited by 545
- Algebra.IsAlgebraicstatement and proof · cited by 322
- Transcendentalstatement and proof · cited by 91
- IsAlgebraic.restrictScalarsproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicIndependent.extendScalarsproof · cited by 4
- Algebra.IsAlgebraic.transcendental_iffproof · cited by 1
- Transcendental.subalgebraAlgebraicClosureproof · cited by 0
- Transcendental.algebraicClosureproof · cited by 0