Theorems · Theorem · group theory
finite_irreducible
∀ {M : Type u_1} [inst : CommMonoid M] [Subsingleton Mˣ] [Monoid.FG M], {p | Irreducible p}.FiniteA finitely generated monoid with a single unit has finitely many irreducible elements.
- Defined in
- Mathlib.Algebra.AffineMonoid.Irreducible
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredstatement and proof · cited by 6,101
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- Set.Finitestatement and proof · cited by 1,814
- Irreduciblestatement and proof · cited by 496
- Monoid.FGstatement and proof · cited by 19
- Monoid.FG.fg_topproof · cited by 7
- Submonoid.FG.finite_irreducible_mem_submonoidClosureproof · cited by 1
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