Theorems · Definition · commutative algebra

Algebra.SubmersivePresentation.comp

{R : Type u} →
  {S : Type v} →
    {ι : Type w} →
      {σ : Type t} →
        [inst : CommRing R] →
          [inst_1 : CommRing S] →
            [inst_2 : Algebra R S] →
              [inst_3 : Finite σ] →
                {T : Type u_1} →
                  {ι' : Type u_2} →
                    {σ' : Type u_3} →
                      [inst_4 : CommRing T] →
                        [inst_5 : Algebra R T] →
                          [inst_6 : Algebra S T] →
                            [IsScalarTower R S T] →
                              [inst_8 : Finite σ'] →
                                Algebra.SubmersivePresentation S T ι' σ' →
                                  Algebra.SubmersivePresentation R S ι σ →
                                    Algebra.SubmersivePresentation R T (ι' ⊕ ι) (σ' ⊕ σ)

Given an R-algebra S and an S-algebra T with submersive presentations, this is the canonical submersive presentation of T as an R-algebra.

Defined in

Mathlib.RingTheory.Extension.Presentation.Submersive

Cited by

2 results in Mathlib

Foundations

Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFiniteCommRingAlgebraAlgebraIsScalarTowerFinite