Theorems · Inductive type · commutative algebra

Algebra.Presentation.HasCoeffs

{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] →
              Algebra.Presentation R S ι σ →
                (R₀ : Type u_5) →
                  [inst_3 : CommRing R₀] →
                    [inst_4 : Algebra R₀ R] → [inst_5 : Algebra R₀ S] → [IsScalarTower R₀ R S] → Prop

A ring R₀ has the coefficients of the presentation P if the coefficients of the relations of P lie in the image of R₀ in R. The smallest subring of R satisfying this is given by Algebra.Presentation.Core P.

Defined in

Mathlib.RingTheory.Extension.Presentation.Core

Cited by

23 results in Mathlib

Foundations

Depth 7 from the axioms · uses no axioms

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTower