Theorems · Theorem · algebraic geometry
PrimeSpectrum.isIntegral_of_isClosedMap_comap_mapRingHom
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] (f : R →+* S),
IsClosedMap (PrimeSpectrum.comap (Polynomial.mapRingHom f)) → f.IsIntegral- Cited by
- 1 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites88
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebraproof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Polynomialstatement and proof · cited by 5,681
- Set.imageproof · cited by 5,609
- Idealproof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsIntegralHom.iff_universallyClosed_and_isAffineHomproof · cited by 2