Theorems · Theorem · group theory
Submonoid.FG.finite_irreducible_mem_submonoidClosure
∀ {M : Type u_1} [inst : CommMonoid M] [Subsingleton Mˣ] {S : Submonoid M}, S.FG → {p | p ∈ S ∧ Irreducible p}.FiniteA finitely generated submonoid of a monoid with a single unit has finitely many irreducible elements.
- Defined in
- Mathlib.Algebra.AffineMonoid.Irreducible
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidSubsingleton
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.ofPredstatement · cited by 6,101
- Submonoidstatement and proof · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- Set.Finitestatement · cited by 1,814
- Irreduciblestatement · cited by 496
- Set.Finite.subsetproof · cited by 285
- Finset.finite_toSetproof · cited by 210
- Submonoid.closureproof · cited by 167
- Submonoid.FGstatement and proof · cited by 24
Cited by1
Results whose statement or proof uses this declaration.
- finite_irreducibleproof · cited by 0