Theorems · Theorem · commutative algebra
IsLocalization.Away.of_associated
∀ {R : Type u_1} [inst : CommSemiring R] {S : Type u_2} [inst_1 : CommSemiring S] [inst_2 : Algebra R S] {r r' : R},
Associated r r' → ∀ [IsLocalization.Away r S], IsLocalization.Away r' S- Cited by
- 6 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomproof · cited by 10,189
- Algebra.algebraMapproof · cited by 4,706
- Monoidproof · cited by 3,887
- Unitsproof · cited by 2,804
- FunLikeproof · cited by 2,560
- mul_commproof · cited by 2,262
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
- IsUnitproof · cited by 1,602
Cited by6
Results whose statement or proof uses this declaration.
- Algebra.IsLocalIso.of_span_range_eq_topproof · cited by 3
- Algebra.IsStandardEtale.of_isLocalizationAwayproof · cited by 2
- Algebra.IsStandardOpenImmersion.transproof · cited by 2
- RingHom.locally_ofLocalizationSpanTargetproof · cited by 1
- IsLocalization.Away.iff_of_associatedproof · cited by 1
- Algebra.IsSmoothAt.exists_isStandardEtale_mvPolynomialproof · cited by 1