中文摘要：

结构上像树的代数学由 Loday 定义的 A 做给在他们的和是联合的意义的关联性的由二部合成的切开的二个二进制手术。类似的结构上像树的类型代数学与三部分、四部关联性切开以后被获得。这些结构能也从合适的线性操作员的行动被导出，例如一个 Rota-Baxter 操作员或 TD 操作员，在联合代数学上。由发现关联性的五部分的切开激发了，我们考虑 Rota-Baxter TD (RBTD ) 操作员，联合 Rota-Baxter 操作员，并且在联合代数学上有关线性操作员来自花名册问题的最近的研究的一个操作员和 TD 操作员。生根的森林上的免费 RBTD 代数学被构造。我们然后介绍它的定义关系被一个 RBTD 操作员的行动描绘的 quinquedendriform 代数学和表演的概念，类似于格结构上像树并且 tridendriform 代数学。

英文摘要：

A dendriform algebra defined by Loday has two binary operations that give a two-part splitting of the associativity in the sense that their sum is associative. Sim- ilar dendriform type algebras with three-part and four-part splitting of the associativity were later obtained. These structures can also be derived from actions of suitable linear operators, such as a Rota-Baxter operator or TD operator, on an associative algebra. Mo- tivated by finding a five-part splitting of the associativity, we consider the Rota-Baxter TD （RBTD） operator, an operator combining the Rota-Baxter operator and TD oper- ator, and coming from a recent study of Rota＇s problem concerning linear operators on associative algebras. Free RBTD algebras on rooted forests are constructed. We then introduce the concept of a quinquedendriform algebra and show that its defining relations are characterized by the action of an RBTD operator, similar to the cases of dendriform and tridendriform algebras.