Theorems · Definition · group theory

DirectSum.SetLike.IsHomogeneous

{ι : Type u_1} →
  {M : Type u_3} →
    {σ : Type u_4} →
      [inst : DecidableEq ι] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : SetLike σ M] →
            [inst_3 : AddSubmonoidClass σ M] →
              (ℳ : ι → σ) → [DirectSum.Decomposition ℳ] → {P : Type u_5} → [SetLike P M] → P → Prop

A substructure p ⊆ M is homogeneous if for every m ∈ p, all homogeneous components of m are in p.

Defined in

Mathlib.Algebra.DirectSum.Decomposition

Cited by

14 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqAddCommMonoidSetLikeAddSubmonoidClassDirectSum.DecompositionSetLike