Theorems · Theorem · commutative algebra

IsLocalization.lift_unique

∀ {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] [inst_4 : IsLocalization M S] {g : R →+* P}
  (hg : ∀ (y : ↥M), IsUnit (g ↑y)) {j : S →+* P}, (∀ (x : R), j ((algebraMap R S) x) = g x) → IsLocalization.lift hg = j

Defined in

Mathlib.RingTheory.Localization.Defs

Cited by

3 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraCommSemiringIsLocalization