A classification of module braces over the ring of $\mathbf{p}$-adic integers
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Aragona, Riccardo Gavioli, Norberto Nozzi, Giuseppe |
| author_facet | Aragona, Riccardo Gavioli, Norberto Nozzi, Giuseppe |
| contents | In this paper we study the $R$-braces $(M,+,\circ)$ such that $M\cdot M$ is cyclic, where $R$ is the ring of $p$-adic and $\cdot$ is the product of the radical $R$-algebra associated to $M$. In particular, we give a classification up to isomorphism in the torsion-free case and up to isoclinism in the torsion case. More precisely, the isomorphism classes and the isoclinism classes of such radical algebras are in correspondence with particular equivalence classes of the bilinear forms defined starting from the products of the algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04925 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A classification of module braces over the ring of $\mathbf{p}$-adic integers Aragona, Riccardo Gavioli, Norberto Nozzi, Giuseppe Group Theory Rings and Algebras 16N20, 20N99, 20B35, 20K30, 15A63, 11E08 In this paper we study the $R$-braces $(M,+,\circ)$ such that $M\cdot M$ is cyclic, where $R$ is the ring of $p$-adic and $\cdot$ is the product of the radical $R$-algebra associated to $M$. In particular, we give a classification up to isomorphism in the torsion-free case and up to isoclinism in the torsion case. More precisely, the isomorphism classes and the isoclinism classes of such radical algebras are in correspondence with particular equivalence classes of the bilinear forms defined starting from the products of the algebras. |
| title | A classification of module braces over the ring of $\mathbf{p}$-adic integers |
| topic | Group Theory Rings and Algebras 16N20, 20N99, 20B35, 20K30, 15A63, 11E08 |
| url | https://arxiv.org/abs/2406.04925 |