Theorems · Theorem · commutative algebra
IsLocalization.Away.iff_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)If r and r' are associated elements of R, an R-algebra S
is the localization of R away from r if and only if it is the localization of R away from
r'.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Associatedstatement and proof · cited by 296
- IsLocalization.Awaystatement and proof · cited by 218
- Associated.symmproof · cited by 87
- IsLocalization.Away.of_associatedproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalization.Away.mul_of_associatedproof · cited by 1