Theorems · Theorem · commutative algebra
RingHom.rangeRestrict_surjective
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] (f : R →+* S),
Function.Surjective ⇑f.rangeRestrict- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRingNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- RingHomstatement and proof · cited by 10,189
- Subringstatement · cited by 602
- NonAssocRingstatement and proof · cited by 483
- RingHom.rangestatement and proof · cited by 138
- RingHom.rangeRestrictstatement and proof · cited by 13
- RingHom.mem_rangeproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.eq_zero_of_polynomial_mem_map_rangeproof · cited by 1
- CommRingCat.essentiallySmall_of_localizationAwayproof · cited by 1
- Polynomial.isJacobsonRing_polynomial_of_isJacobsonRingproof · cited by 1