Theorems · Theorem · commutative algebra
IsLocalization.away_of_isIdempotentElem
∀ {R : Type u_4} {S : Type u_5} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {e : R},
IsIdempotentElem e →
RingHom.ker (algebraMap R S) = Ideal.span {1 - e} → Function.Surjective ⇑(algebraMap R S) → IsLocalization.Away e S- Cited by
- 4 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- mul_commproof · cited by 2,262
- Ideal.spanstatement and proof · cited by 948
- map_subproof · cited by 565
- sub_eq_zeroproof · cited by 407
Cited by4
Results whose statement or proof uses this declaration.
- Algebra.IsStandardEtale.of_surjectiveproof · cited by 1
- AlgebraicGeometry.isOpenImmersion_SpecMap_iff_of_surjectiveproof · cited by 0
- IsLocalization.Away.quotient_of_isIdempotentElemproof · cited by 0
- Algebra.IsLocalIso.pi_of_finiteproof · cited by 0