Theorems · Definition · commutative algebra

Algebra.Presentation.quotientEquiv

{R : Type u} →
  {S : Type v} →
    {ι : Type w} →
      {σ : Type t} →
        [inst : CommRing R] →
          [inst_1 : CommRing S] → [inst_2 : Algebra R S] → (P : Algebra.Presentation R S ι σ) → P.Quotient ≃ₐ[P.Ring] S

P.Quotient is P.Ring-isomorphic to S and in particular R-isomorphic to S.

Defined in

Mathlib.RingTheory.Extension.Presentation.Basic

Cited by

5 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra