Theorems · Theorem · commutative algebra
Algebra.isGeometricallyReduced_iff
∀ (R : Type u_3) (A : Type u_4) [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A],
Algebra.IsGeometricallyReduced R A ↔
∀ (p : Ideal R) [inst_3 : p.IsPrime], IsReduced (TensorProduct R (AlgebraicClosure p.ResidueField) A)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- TensorProductstatement and proof · cited by 2,545
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.primeComplstatement · cited by 462
- Localization.AtPrimestatement · cited by 299
- Ideal.ResidueFieldstatement and proof · cited by 119
- IsReducedstatement and proof · cited by 98
- AlgebraicClosurestatement and proof · cited by 53
- Algebra.IsGeometricallyReducedstatement and proof · cited by 5
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