拟对称函数与罗巴代数是两个理论深刻、应用广泛的代数对象，二者关系密切。本项目首先将拟对称函数推广为半群幂拟对称函数，借以给出自由罗巴代数一种新的结构表示。然后在此基础上研究罗巴理想的结构，刻画罗巴环的特征， 给出一类满足升链条件的罗巴理想，并研究半群幂对称和拟对称函数代数各种基之间的关系及其在罗巴代数中的表现，给出罗巴代数、半群幂对称和拟对称函数代数及其对偶代数之间的关系。最后研究在上述过程中自然产生的带二项式系数的多重zeta值的代数性质与基本乘法公式。

A very close relationship exists between Rota-Baxter algebras and the algebra of quasi-symmetric functions, which are two important objects with profound theories and broad applications. In this research item, we plan to construct free Rota-Baxter algebras by generalizing quasi-symmetric functions to the quasi-symmetric functions with semigroup exponents. And then we investigate Rota-Baxter ideals by using this structure to classify the characteristic of Rota-Baxter rings and give a class of Rota-Baxter ideals satisfying ascending condition. In particular, we will study various bases for the algebra of the new symmetric and quasi-symmetric functions and their correspondence in Rota-Baxter algebras, and the relationships between these algebras and their dual will also be considered. Finally, we investigate the algebraic properties and product formulas for multiple zeta values with binomial coefficients which arises naturally in our study.