Author

Liam Baker

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Preprint Oct 2026

Prime-Power Multiplicative Modular Monoid Morphisms

We undertake a systematic study of multiplicative monoid morphisms between prime-power modular monoids $(\mathbb{Z}/p^e\mathbb{Z},\cdot)$ and $(\mathbb{Z}/q^f\mathbb{Z},\cdot)$, for arbitrary primes $p,q$ and integers $e,f\geq 1$. Our approach proceeds in three stages. We first determine the hom-set $\mathbf{Hom}(U_{p^...

Joseph Atalaye, Liam Baker, Sophie Marques · 0 citations

Preprint Sep 2026

Direct-product rigidity and factor reconstruction for monoids with zero

We study direct products of monoids with zero and give a criterion under which their factors can be recovered from the multiplicative structure alone. While classical decomposition theory encodes direct products through factor congruences, central elements, and refinement properties, we give a concrete multiplicative r...

Joseph Atalaye, Liam Baker, Sophie Marques · 0 citations