Theorems · Theorem · commutative algebra

Algebra.isLocalization_iff_isPushout

∀ {R : Type u_1} [inst : CommSemiring R] (S : Submonoid R) (A : Type u_2) [inst_1 : CommSemiring A]
  [inst_2 : Algebra R A] [IsLocalization S A] {T : Type u_5} {B : Type u_6} [inst_4 : CommSemiring T]
  [inst_5 : CommSemiring B] [inst_6 : Algebra R T] [inst_7 : Algebra T B] [inst_8 : Algebra R B] [inst_9 : Algebra A B]
  [inst_10 : IsScalarTower R T B] [inst_11 : IsScalarTower R A B],
  IsLocalization (Algebra.algebraMapSubmonoid T S) B ↔ Algebra.IsPushout R T A B

Defined in

Mathlib.RingTheory.Localization.BaseChange

Cited by

4 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraIsLocalizationCommSemiringCommSemiringAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower