Theorems · Definition · commutative algebra

Module.Presentation.restrictScalars

{B : Type u_1} →
  [inst : Ring B] →
    {M : Type u_2} →
      [inst_1 : AddCommGroup M] →
        [inst_2 : Module B M] →
          [inst_3 : DecidableEq B] →
            (presM : Module.Presentation B M) →
              [inst_4 : DecidableEq presM.G] →
                {A : Type u_3} →
                  [inst_5 : CommRing A] →
                    [inst_6 : Algebra A B] →
                      [inst_7 : Module A M] →
                        [IsScalarTower A B M] →
                          (presB : Module.Presentation A B) → presM.RestrictScalarsData presB → Module.Presentation A M

A presentation of the restriction of scalars from B to A of a B-module M, given a presentation of M as a B-module, a presentation of B as an A-module, and an additional data.

Defined in

Mathlib.Algebra.Module.Presentation.RestrictScalars

Cited by

0 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleDecidableEqDecidableEqCommRingAlgebraModuleIsScalarTower