Theorems · Theorem · commutative algebra
IsLocalization.eq_iff_eq
∀ {R : Type u_1} [inst : CommSemiring R] {M : Submonoid R} {S : Type u_2} [inst_1 : CommSemiring S]
[inst_2 : Algebra R S] {P : Type u_3} [inst_3 : CommSemiring P] [IsLocalization M S] [inst_5 : Algebra R P]
[IsLocalization M P] {x y : R}, (algebraMap R S) x = (algebraMap R S) y ↔ (algebraMap R P) x = (algebraMap R P) y- Defined in
- Mathlib.RingTheory.Localization.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
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- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- IsLocalization.toLocalizationMapproof · cited by 69
- Submonoid.LocalizationMap.eq_iff_eqproof · cited by 1
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