Theorems · Theorem · commutative algebra
Algebra.isGeometricallyReduced_field_iff
∀ (k : Type u_3) (A : Type u_4) [inst : Field k] [inst_1 : Ring A] [inst_2 : Algebra k A], Algebra.IsGeometricallyReduced k A ↔ IsReduced (TensorProduct k (AlgebraicClosure k) A)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Idealproof · cited by 4,748
- Bot.botproof · cited by 4,720
- TensorProductstatement and proof · cited by 2,545
- AlgEquivproof · cited by 1,681
- Ideal.IsPrimeproof · cited by 827
- AlgEquiv.symmproof · cited by 615
- Algebra.IsAlgebraicproof · cited by 322
- Ideal.ResidueFieldproof · cited by 119
- IsReducedstatement and proof · cited by 98
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.IsGeometricallyReduced.of_injectiveproof · cited by 0