Reutenauer

Irreducibility of Semigroup Morphisms

arXiv:2603.15177v2 Announce Type: replace Abstract: We introduce and study the notion of irreducibility of semigroup morphisms over a finite alphabet. Given an alphabet $\Sigma$, a morphism $\varphi:\Sigma^+\rightarrow\Sigma^+$ is irreducible if any factorisation $\varphi=\psi_2\circ\psi_1$ can only be satisfied if $\psi_1$ or $\psi_2$ is a trivial morphism; otherwise, $\varphi$ is reducible. This definition provides a notion of primality in the endomorphism monoid of the free semigroup -- a...