A morphism on a free semigroup is irreducible exactly when its image words admit no nontrivial factor basis; the paper proves this and related factorization results.
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Irreducibility of Endomorphisms of Finitely Generated Free Semigroups
A morphism on a free semigroup is irreducible exactly when its image words admit no nontrivial factor basis; the paper proves this and related factorization results.