Theorems · Definition · commutative algebra
RingHom.eqLocus
{R : Type u} → [inst : NonAssocRing R] → {S : Type v} → [inst_1 : Semiring S] → (R →+* S) → (R →+* S) → Subring RThe subring of elements x : R such that f x = g x, i.e.,
the equalizer of f and g as a subring of R
- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
- Assumes
- NonAssocRingSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Set.ofPredproof · cited by 6,101
- AddSubgroupproof · cited by 3,232
- Submonoidproof · cited by 3,086
- Subringstatement · cited by 602
- NonAssocRingstatement and proof · cited by 483
- MonoidHomClass.toMonoidHomproof · cited by 294
- AddMonoidHomClass.toAddMonoidHomproof · cited by 232
- MonoidHom.eqLocusMproof · cited by 5
- AddMonoidHom.eqLocusproof · cited by 2
Cited by20
Results whose statement or proof uses this declaration.
- TopCat.Sheaf.objSupIsoProdEqLocusstatement · cited by 6
- RingHom.pullbackproof · cited by 6
- CommRingCat.pullbackConeIsLimitproof · cited by 4
- Algebra.codRestrictEqLocusPushoutCoconeproof · cited by 3
- CommRingCat.equalizerForkproof · cited by 3
- RingHom.eqLocusFieldproof · cited by 2
- Algebra.IsEffective.eqLocus_includeLeft_includeRightstatement and proof · cited by 1
- TopCat.Sheaf.objSupIsoProdEqLocus_inv_eq_iffstatement and proof · cited by 1
- TopCat.Sheaf.objSupIsoProdEqLocus_inv_fststatement and proof · cited by 1
- TopCat.Sheaf.objSupIsoProdEqLocus_inv_sndstatement and proof · cited by 1
- Algebra.codRestrictEqLocusPushoutCocone.surjective_of_isEffectiveproof · cited by 1
- RingHom.eqOn_set_closureproof · cited by 1