Theorems · Theorem · commutative algebra
Algebra.Smooth.exists_subalgebra_finiteType
Deprecated since 2026-01-07Use Algebra.Smooth.exists_subalgebra_fg instead.
∀ (R : Type u_1) [inst : CommRing R] (A : Type u) (B : Type u_2) [inst_1 : CommRing A] [inst_2 : Algebra R A] [inst_3 : CommRing B] [inst_4 : Algebra A B] [Algebra.Smooth A B], ∃ A₀ B₀ x x_1, Algebra.FiniteType R ↥A₀ ∧ Algebra.Smooth (↥A₀) B₀ ∧ Nonempty (B ≃ₐ[A] TensorProduct (↥A₀) A B₀)
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- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
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- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- TensorProductstatement and proof · cited by 2,545
- AlgEquivstatement and proof · cited by 1,681
- Subalgebrastatement and proof · cited by 1,353
- Algebra.FiniteTypestatement · cited by 84
- Subalgebra.FGproof · cited by 45
- Algebra.Smoothstatement and proof · cited by 22
- Subalgebra.fg_iff_finiteTypeproof · cited by 2
- Algebra.Smooth.exists_subalgebra_fgproof · cited by 2
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