Theorems · Definition · commutative algebra

Module.IsTorsionBy.hasSMul

{R : Type u_1} →
  {M : Type u_2} →
    [inst : Ring R] →
      [inst_1 : AddCommGroup M] →
        [inst_2 : Module R M] → {r : R} → Module.IsTorsionBy R M r → SMul (R ⧸ Ideal.span {r}) M

can't be an instance because hM can't be inferred

Defined in: Mathlib.Algebra.Module.Torsion.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring AddCommGroup Module

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Ringstatement and proof · cited by 7,463
Idealstatement · cited by 4,748
HasQuotient.Quotientstatement · cited by 2,301
Ideal.spanstatement · cited by 948
Module.IsTorsionBystatement and proof · cited by 15
Module.IsTorsionBySet.hasSMulproof · cited by 1

Cited by1

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Module.IsTorsionBy.mk_smulstatement · cited by 0