Theorems · Theorem · commutative algebra
IsStronglyTranscendental.of_isLocalization
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[inst_3 : CommRing T] [inst_4 : Algebra R T] [inst_5 : Algebra S T] (M : Submonoid S) [IsLocalization M T]
[IsScalarTower R S T] {x : S}, IsStronglyTranscendental R x → IsStronglyTranscendental R ((algebraMap S T) x)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Semiringproof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringproof · cited by 10,911
- RingHomstatement · cited by 10,189
- Polynomialproof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- Submonoidstatement and proof · cited by 3,086
- mul_commproof · cited by 2,262
- Nat.cast_zeroproof · cited by 1,870
Cited by1
Results whose statement or proof uses this declaration.
- IsStronglyTranscendental.iff_of_isLocalizationproof · cited by 1