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math.RA2026
Direct-product rigidity and factor reconstruction for monoids with zero
Joseph Atalaye, Liam Baker, Sophie Marques
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…
math.RA2026
Automorphism groups of direct products of multiplicative monoids of certain rings
Joseph Atalaye, Liam Baker, Sophie Marques
In this paper, we establish a rigidity result for automorphisms of multiplicative direct products of -rings which are total ring of fraction that have pairwise distinct cardinal…
math.RA2024
On the automorphism group of the monoid of the integers modulo a prime power
Joseph Atalaye, Liam Baker, Sophie Marques
This paper determines the structure of the automorphism group of the unit group \((U_{p^e}, \cdot)\) and the monoid \((\mathbb{Z}/p^e \mathbb{Z}, \cdot)\). For \( e \geq 5 \), we e…