Theorems · Definition · commutative algebra

Algebra.Presentation.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] →
              {ι' : Type u_1} →
                {σ' : Type u_2} →
                  {T : Type u_3} →
                    [inst_3 : CommRing T] →
                      [inst_4 : Algebra S T] →
                        Algebra.Presentation S T ι' σ' →
                          Algebra.Presentation R S ι σ →
                            [inst_5 : Algebra R T] → [IsScalarTower R S T] → Algebra.Presentation R T (ι' ⊕ ι) (σ' ⊕ σ)

Given presentations of T over S and of S over R, we may construct a presentation of T over R.

Defined in

Mathlib.RingTheory.Extension.Presentation.Basic

Cited by

7 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTower