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Theorems · Definition · commutative algebra

RingHom.eqLocus

{R : Type u} → [inst : NonAssocRing R] → {S : Type v} → [inst_1 : Semiring S] → (R →+* S) → (R →+* S) → Subring R

The 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.

TopCat.Sheaf.objSupIsoProdEqLocus · cited by 6Sheaf.objSupIsoProdEqLocusRingHom.pullback · cited by 6RingHom.pullbackCommRingCat.pullbackConeIsLimit · cited by 4CommRingCat.pullbackConeI…Algebra.codRestrictEqLocusPushoutCocone · cited by 3Algebra.codRestrictEqLocu…CommRingCat.equalizerFork · cited by 3CommRingCat.equalizerForkRingHom.eqLocusField · cited by 2RingHom.eqLocusFieldAlgebra.IsEffective.eqLocus_includeLeft_includeRight · cited by 1IsEffective.eqLocus_inclu…TopCat.Sheaf.objSupIsoProdEqLocus_inv_eq_iff · cited by 1Sheaf.objSupIsoProdEqLocu…TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst · cited by 1Sheaf.objSupIsoProdEqLocu…TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd · cited by 1Sheaf.objSupIsoProdEqLocu…Algebra.codRestrictEqLocusPushoutCocone.surjective_of_isEffective · cited by 1codRestrictEqLocusPushout…RingHom.eqOn_set_closure · cited by 1RingHom.eqOn_set_closureRingHom.isUnit_eqLocus_mk_iff · cited by 1RingHom.isUnit_eqLocus_mk…RingHom.mem_eqLocus · cited by 0RingHom.mem_eqLocusTopCat.Sheaf.objSupIsoProdEqLocus_hom_fst · cited by 0Sheaf.objSupIsoProdEqLocu…DFunLike.coe · cited by 62936DFunLike.coeSemiring · cited by 13802SemiringRingHom · cited by 10189RingHomSet.ofPred · cited by 6101Set.ofPredAddSubgroup · cited by 3232AddSubgroupSubmonoid · cited by 3086SubmonoidSubring · cited by 602SubringNonAssocRing · cited by 483NonAssocRingMonoidHomClass.toMonoidHom · cited by 294MonoidHomClass.toMonoidHomAddMonoidHomClass.toAddMonoidHom · cited by 232AddMonoidHomClass.toAddMo…MonoidHom.eqLocusM · cited by 5MonoidHom.eqLocusMAddMonoidHom.eqLocus · cited by 2AddMonoidHom.eqLocusRingHom.eqLocusCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by20

Results whose statement or proof uses this declaration.