Theorems · Theorem · commutative algebra
IsStronglyTranscendental.of_map
∀ {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] {x : S} {f : S →ₐ[R] T},
Function.Injective ⇑f → IsStronglyTranscendental R (f x) → IsStronglyTranscendental R x- Cited by
- 2 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.
Cites25
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
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement and proof · cited by 3,236
- map_zeroproof · cited by 1,614
- Polynomial.Cproof · cited by 1,598
- map_mulproof · cited by 1,137
- Polynomial.mapproof · cited by 806
- RingHomClass.toRingHomproof · cited by 746
Cited by2
Results whose statement or proof uses this declaration.
- IsStronglyTranscendental.iff_of_isLocalizationproof · cited by 1
- IsStronglyTranscendental.of_transcendentalproof · cited by 0