Theorems · Definition · commutative algebra
RingHom.rangeS
{R : Type u} → {S : Type v} → [inst : NonAssocSemiring R] → [inst_1 : NonAssocSemiring S] → (R →+* S) → Subsemiring SThe range of a ring homomorphism is a subsemiring. See Note [range copy pattern].
- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
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.coeproof · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- Top.topproof · cited by 9,680
- Set.rangeproof · cited by 4,705
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement · cited by 456
- Subsemiring.mapproof · cited by 29
- Subsemiring.copyproof · cited by 5
Cited by57
Results whose statement or proof uses this declaration.
- AlgHom.rangeproof · cited by 169
- IsLocalization.IsIntegerproof · cited by 39
- Polynomial.liftsproof · cited by 35
- RingHom.coe_rangeSstatement and proof · cited by 6
- RingHom.rangeS_top_of_surjectivestatement · cited by 5
- RingHom.mem_rangeSstatement · cited by 4
- RingHom.rangeSRestrictstatement and proof · cited by 4
- RingCon.quotientKerEquivRangeₐproof · cited by 4
- Polynomial.mem_map_rangeSstatement and proof · cited by 4
- IsLocalization.isInteger_addproof · cited by 3
- RingCon.comapQuotientEquivRangeSstatement · cited by 3
- RingHom.mem_rangeS_selfstatement · cited by 2