Theorems · Theorem · commutative algebra
StandardEtalePresentation.exists_mul_aeval_x_g_pow_eq_aeval_x
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
(P : StandardEtalePresentation R S) (x : S), ∃ p n, x * (Polynomial.aeval P.x) P.g ^ n = (Polynomial.aeval P.x) p- Defined in
- Mathlib.RingTheory.Etale.StandardEtale
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites39
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
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- map_mulproof · cited by 1,137
- AlgEquiv.symmproof · cited by 615
- Polynomial.aevalstatement and proof · cited by 615
- map_powproof · cited by 503
- Submonoid.powersproof · cited by 408
- AdjoinRootproof · cited by 177
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.IsStandardEtale.of_isLocalizationAwayproof · cited by 2