Theorems · Theorem · commutative algebra
IsLocalization.isUnit_comp
∀ {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] (j : S →+* P) (y : ↥M),
IsUnit ((j.comp (algebraMap R S)) ↑y)- Defined in
- Mathlib.RingTheory.Localization.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- IsUnitstatement · cited by 1,602
- RingHom.compstatement · cited by 899
- IsLocalizationstatement and proof · cited by 636
- RingHom.toMonoidHomproof · cited by 132
- IsLocalization.toLocalizationMapproof · cited by 69
- Submonoid.LocalizationMap.isUnit_compproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalization.lift_of_compstatement · cited by 1
- IsLocalization.injective_iff_map_algebraMap_eqproof · cited by 1