Theorems · Theorem · algebraic geometry
RingHom.IsIntegral.comap_surjective
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S},
f.IsIntegral → Function.Injective ⇑f → Function.Surjective (PrimeSpectrum.comap f)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebraproof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- PrimeSpectrumstatement · cited by 625
- FaithfulSMulproof · cited by 340
- RingHom.toAlgebraproof · cited by 337
- PrimeSpectrum.comapstatement · cited by 199
- RingHom.IsIntegralstatement and proof · cited by 54
- faithfulSMul_iff_algebraMap_injectiveproof · cited by 17
- Algebra.IsIntegral.comap_surjectiveproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isHomeomorph_comapproof · cited by 1