Theorems · Definition · commutative algebra

Module.AEval.mapSubmodule

(R : Type u_1) →
  {A : Type u_2} →
    (M : Type u_3) →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          (a : A) →
            [inst_2 : Algebra R A] →
              [inst_3 : AddCommMonoid M] →
                [inst_4 : Module A M] →
                  [inst_5 : Module R M] →
                    [inst_6 : IsScalarTower R A M] →
                      ↥((Algebra.lsmul R R M) a).invtSubmodule ≃o Submodule (Polynomial R) (Module.AEval R M a)

The natural order isomorphism between the two ways to represent invariant submodules.

Defined in

Mathlib.Algebra.Polynomial.Module.AEval

Cited by

5 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTower