Mathlib Map

Theorems · Definition · commutative algebra

Algebra.Presentation.ofFinitePresentation

(R : Type u) →
  (S : Type v) →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] →
          [inst_3 : Algebra.FinitePresentation R S] →
            Algebra.Presentation R S (Fin (Algebra.Presentation.ofFinitePresentationVars R S))
              (Fin (Algebra.Presentation.ofFinitePresentationRels R S))

An arbitrary choice of a finite presentation of a finitely presented algebra.

Defined in
Mathlib.RingTheory.Extension.Presentation.Basic
Cited by
1 results in Mathlib
Foundations
Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraAlgebra.FinitePresentation
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Algebra.Smooth.exists_subalgebra_fg · cited by 2Smooth.exists_subalgebra_…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraNonempty.some · cited by 340Nonempty.someAlgebra.Presentation · cited by 70Algebra.PresentationAlgebra.FinitePresentation · cited by 56Algebra.FinitePresentationAlgebra.Presentation.ofFinitePresentationRels · cited by 1Presentation.ofFinitePres…Algebra.Presentation.ofFinitePresentationVars · cited by 1Presentation.ofFinitePres…Presentation.ofFinitePresenta…CITED BYCITES

Cites7

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

Cited by1

Results whose statement or proof uses this declaration.