Theorems · Theorem · commutative algebra
RingHom.Flat.generalizingMap_comap
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S},
f.Flat → GeneralizingMap (PrimeSpectrum.comap f)Spec S → Spec R is generalizing if R →+* S is flat.
- Defined in
- Mathlib.RingTheory.RingHom.Flat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Algebraproof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- PrimeSpectrumstatement · cited by 625
- RingHom.toAlgebraproof · cited by 337
- PrimeSpectrum.comapstatement · cited by 199
- RingHom.Flatstatement and proof · cited by 60
- GeneralizingMapstatement · cited by 16
- Algebra.HasGoingDown.iff_generalizingMap_primeSpectrumComapproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Flat.isQuotientMap_of_surjectiveproof · cited by 1