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arXiv · 2605.06119

Automorphism groups of direct products of multiplicative monoids of certain rings

Joseph Atalaye·Liam Baker·Sophie Marques
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Abstract

In this paper, we establish a rigidity result for automorphisms of multiplicative direct products of $D$-rings which are total ring of fraction that have pairwise distinct cardinalities. Under these assumptions, every automorphism acts independently on each factor, so that no interaction between distinct components occurs; in particular, the automorphism group decomposes canonically as the direct product of the automorphism groups of the factors. As a consequence, the automorphism group of the multiplicative monoid of integers modulo $n$ is entirely determined by its $p$-power components.

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Joseph Atalaye, Liam Baker, Sophie Marques. 2026-05-07. Automorphism groups of direct products of multiplicative monoids of certain rings. https://arxiv.org/abs/2605.06119

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