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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.18049 |
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| _version_ | 1866909440028966912 |
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| author | Guan, Zhipeng Zhang, Chi |
| author_facet | Guan, Zhipeng Zhang, Chi |
| contents | Let $\mathcal{R}$ be a commutative ring with unity, and let $P$ be a locally finite poset. The aim of the paper is to provide an explicit description of the additive biderivations of the incidence algebra $I(P, \mathcal{R})$. We demonstrate that every additive biderivation is the sum of several inner biderivations and extremal biderivations. Furthermore, if the number of elements in any maximal chain in $P$ is infinite, every additive biderivation of $I(P,\mathcal{R})$ is the sum of several inner biderivations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18049 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Additive Biderivations of Incidence Algebras Guan, Zhipeng Zhang, Chi Rings and Algebras Primiary 16W25, 15A78, Secondary 05B20, 16S60 Let $\mathcal{R}$ be a commutative ring with unity, and let $P$ be a locally finite poset. The aim of the paper is to provide an explicit description of the additive biderivations of the incidence algebra $I(P, \mathcal{R})$. We demonstrate that every additive biderivation is the sum of several inner biderivations and extremal biderivations. Furthermore, if the number of elements in any maximal chain in $P$ is infinite, every additive biderivation of $I(P,\mathcal{R})$ is the sum of several inner biderivations. |
| title | Additive Biderivations of Incidence Algebras |
| topic | Rings and Algebras Primiary 16W25, 15A78, Secondary 05B20, 16S60 |
| url | https://arxiv.org/abs/2412.18049 |