标题： Rota-Baxter族同态结合代数的结构扩展 显示英文标题

标题： Extending Structures for Rota-Baxter family Hom-associative Algebras

摘要： 在本文中，我们首先定义Rota-Baxter族Hom-结合代数的扩展数据和统一乘积，并理论解决扩展结构问题。此外，我们考虑旗帜数据作为应用，并给出扩展结构问题的一个例子。其次，我们引入Rota-Baxter族Hom-结合代数的匹配对，并理论解决分解问题。最后，我们在Rota-Baxter族Hom扩展结构上定义变形映射，并理论解决分类补集问题。 显示英文摘要

摘要： In this paper, we first define extending datums and unified products of Rota-Baxter family Hom-associative algebras, and theoretically solve the extending structure problem. Moreover, we consider flag datums as an application, and give an example of the extending structure problem. Second, we introduce matched pairs of Rota-Baxter family Hom-associative algebras, and theoretically solve the factorization problem. Finally, we define deformation maps on a Rota-Baxter family Hom extending structure, and theoretically solve the classifying complements problem.