Theorems · Theorem · ring theory
RingHom.surjective
∀ {R₁ : Type u_1} {R₂ : Type u_2} [inst : Semiring R₁] [inst_1 : Semiring R₂] (σ : R₁ →+* R₂) [t : RingHomSurjective σ],
Function.Surjective ⇑σ- Defined in
- Mathlib.Algebra.Ring.CompTypeclasses
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- RingHomSurjectivestatement and proof · cited by 220
- RingHomSurjective.is_surjectiveproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- Bornology.IsVonNBounded.imageproof · cited by 5
- PrimeSpectrum.comap_evalRingHom_basicOpenproof · cited by 2
- IsDedekindDomain.idealFactorsFunOfQuotHom_idstatement and proof · cited by 1
- UniformConvergenceCLM.continuous_of_continuous_uncurryproof · cited by 1
- Ring.map_jacobson_of_ker_leproof · cited by 0
- Algebra.IsLocalIso.pi_of_finiteproof · cited by 0
- Algebra.IsFiniteSplit.exists_tensorProduct_of_etaleproof · cited by 0
- RingHomSurjective.compproof · cited by 0
- idealFactorsFunOfQuotHom_idstatement · cited by 0