Theorems · Definition · commutative algebra

Algebra.SubmersivePresentation.ofHasCoeffs

{R : Type u_1} →
  {S : Type u_2} →
    {ι : Type u_3} →
      {σ : Type u_4} →
        [inst : CommRing R] →
          [inst_1 : CommRing S] →
            [inst_2 : Algebra R S] →
              [inst_3 : Finite σ] →
                (P : Algebra.SubmersivePresentation R S ι σ) →
                  (R₀ : Type u_5) →
                    [inst_4 : CommRing R₀] →
                      [inst_5 : Algebra R₀ R] →
                        [inst_6 : Algebra R₀ S] →
                          [inst_7 : IsScalarTower R₀ R S] →
                            [inst_8 : P.HasCoeffs R₀] →
                              [FaithfulSMul R₀ R] →
                                Algebra.SubmersivePresentation R₀ (Algebra.Presentation.ModelOfHasCoeffs R₀) ι σ

The submersive presentation on P.ModelOfHasCoeffs R₀ provided P.HasCoeffs R₀.

Defined in

Mathlib.RingTheory.Extension.Presentation.Core

Cited by

1 results in Mathlib

Foundations

Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFiniteCommRingAlgebraAlgebraIsScalarTowerAlgebra.SubmersivePresentation.HasCoeffsFaithfulSMul