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Theorems · Definition · commutative algebra

Algebra.Presentation.Quotient

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

The polynomial algebra w.r.t. a family of generators modulo a family of relations.

Defined in
Mathlib.RingTheory.Extension.Presentation.Basic
Cited by
2 results in Mathlib
Foundations
Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Algebra.Presentation.quotientEquiv · cited by 5Presentation.quotientEquivAlgebra.Presentation.quotientEquiv_mk · cited by 1Presentation.quotientEqui…Algebra.Presentation.quotientEquiv_symm · cited by 0Presentation.quotientEqui…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraHasQuotient.Quotient · cited by 2301HasQuotient.QuotientAlgebra.Generators.Ring · cited by 133Generators.RingAlgebra.Presentation.toGenerators · cited by 104Presentation.toGeneratorsAlgebra.Presentation · cited by 70Algebra.PresentationAlgebra.Generators.ker · cited by 46Generators.kerPresentation.QuotientCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.