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arXiv · 2504.16643

Multiple Rota-Baxter algebra and multiple Rota-Baxter modules

Jun He·Xiaosong Peng·Yi Zhang
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Abstract

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.

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Jun He, Xiaosong Peng, Yi Zhang. 2025-04-23. Multiple Rota-Baxter algebra and multiple Rota-Baxter modules. https://arxiv.org/abs/2504.16643

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