Multiplicative Automorphisms of Incidence Algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913217313243136 |
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| author | Kaigorodov, Evgenii Krylov, Piotr Tuganbaev, Askar |
| author_facet | Kaigorodov, Evgenii Krylov, Piotr Tuganbaev, Askar |
| contents | Let $I(X,R)$ be the incidence algebra of the preordered set $X$ over the ring $R$. In the case of a finite connected partially ordered set $X$, we prove that the subgroup of inner multiplicative automorphisms is a direct factor of the group of multiplicative automorphisms of the algebra $I(X,R)$. As a consequence, we obtain several matching criteria of the subgroup of inner multiplicative automorphisms with the group of multiplicative automorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiplicative Automorphisms of Incidence Algebras Kaigorodov, Evgenii Krylov, Piotr Tuganbaev, Askar Rings and Algebras 16W20, 16S50 Let $I(X,R)$ be the incidence algebra of the preordered set $X$ over the ring $R$. In the case of a finite connected partially ordered set $X$, we prove that the subgroup of inner multiplicative automorphisms is a direct factor of the group of multiplicative automorphisms of the algebra $I(X,R)$. As a consequence, we obtain several matching criteria of the subgroup of inner multiplicative automorphisms with the group of multiplicative automorphisms. |
| title | Multiplicative Automorphisms of Incidence Algebras |
| topic | Rings and Algebras 16W20, 16S50 |
| url | https://arxiv.org/abs/2401.17964 |