Multiple Rota-Baxter algebra and multiple Rota-Baxter modules
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908334358003712 |
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| author | He, Jun Peng, Xiaosong Zhang, Yi |
| author_facet | He, Jun Peng, Xiaosong Zhang, Yi |
| contents | In this paper, we develop the theory of multiple Rota-Baxter modules over multiple Rota-Baxter algebras. We introduce left, right, and bimodule structures and construct free $Ω$-operated modules with mixable tensor establishing free commutative multiple Rota-Baxter modules. We provide a necessary and sufficient condition for a free module to admit a free multiple Rota-Baxter module structure. Furthermore, we define projective and injective multiple Rota-Baxter modules, showing that their category has enough projective and injective objects to support derived $\mathrm{Hom}$ functors. Finally, we introduce the tensor product of multiple Rota-Baxter algebras and define flat multiple Rota-Baxter modules, proving that both free and projective modules satisfy the flatness property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiple Rota-Baxter algebra and multiple Rota-Baxter modules He, Jun Peng, Xiaosong Zhang, Yi Rings and Algebras 17B38, 16W99, 05E16, 16S10 In this paper, we develop the theory of multiple Rota-Baxter modules over multiple Rota-Baxter algebras. We introduce left, right, and bimodule structures and construct free $Ω$-operated modules with mixable tensor establishing free commutative multiple Rota-Baxter modules. We provide a necessary and sufficient condition for a free module to admit a free multiple Rota-Baxter module structure. Furthermore, we define projective and injective multiple Rota-Baxter modules, showing that their category has enough projective and injective objects to support derived $\mathrm{Hom}$ functors. Finally, we introduce the tensor product of multiple Rota-Baxter algebras and define flat multiple Rota-Baxter modules, proving that both free and projective modules satisfy the flatness property. |
| title | Multiple Rota-Baxter algebra and multiple Rota-Baxter modules |
| topic | Rings and Algebras 17B38, 16W99, 05E16, 16S10 |
| url | https://arxiv.org/abs/2504.16643 |