Automorphism groups of direct products of multiplicative monoids of certain rings
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917476476911616 |
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| author | Atalaye, Joseph Baker, Liam Marques, Sophie |
| author_facet | Atalaye, Joseph Baker, Liam Marques, Sophie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06119 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Automorphism groups of direct products of multiplicative monoids of certain rings Atalaye, Joseph Baker, Liam Marques, Sophie Rings and Algebras 20B25, 20M32, 20E99, 13H05 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. |
| title | Automorphism groups of direct products of multiplicative monoids of certain rings |
| topic | Rings and Algebras 20B25, 20M32, 20E99, 13H05 |
| url | https://arxiv.org/abs/2605.06119 |