Theorems · Theorem · commutative algebra
IsStronglyTranscendental.of_isLocalization_left
∀ {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 R) [IsLocalization M S]
[IsScalarTower R S T] {x : T}, IsStronglyTranscendental R x → IsStronglyTranscendental S x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- Submonoidstatement and proof · cited by 3,086
- MulZeroClass.mul_zeroproof · cited by 2,091
- mul_assocproof · cited by 1,667
- Polynomial.Cproof · cited by 1,598
- Polynomial.mapproof · cited by 806
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