Theorems · Theorem · algebraic geometry
PrimeSpectrum.comap_injective_of_surjective
∀ {R : Type u} {S : Type v} [inst : CommSemiring R] [inst_1 : CommSemiring S] (f : R →+* S),
Function.Surjective ⇑f → Function.Injective (PrimeSpectrum.comap f)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealproof · cited by 333
- PrimeSpectrum.comapstatement and proof · cited by 199
- PrimeSpectrum.extproof · cited by 43
- Ideal.comap_injective_of_surjectiveproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isClosedEmbedding_comap_of_surjectiveproof · cited by 2
- PrimeSpectrum.isEmbedding_comap_of_surjectiveproof · cited by 2
- PrimeSpectrum.comap_quotientMk_bijective_of_le_nilradicalproof · cited by 1
- Algebra.QuasiFiniteAt.of_isOpen_singletonproof · cited by 1
- chevalley_mvPolynomial_mvPolynomialproof · cited by 0