多项式代数上的罗巴理想  

Rota-Baxter Ideals on Polynomial Algebras

作　　者：谷伟平[1] GU Wei-ping(College of Electromechanical and Information Engineering,Chongqing College of Humanities Science and Technology,Chongqing 401524,China)

机构地区：[1]重庆人文科技学院机电与信息工程学院,重庆401524

出　　处：《南宁师范大学学报（自然科学版）》2021年第4期5-8,共4页Journal of Nanning Normal University：Natural Science Edition

基　　金：重庆人文科技学院一般项目(CRKZK19019)。

摘　　要：设F是一个特征为零的域.刻画了多项式代数F[x]上权为零的单项式罗巴算子对应的罗巴理想的结构,证明了由一个非零多项式f(x)生成的罗巴理想是由f(x)的最低次项生成的理想.Let F be a field with characteristic zero.The classification of Rota-Baxter ideals corresponding to monomial Rota-Baxter operators on the polynomial algebra F[x]is given.When the weight of the Rota-Baxter operator is zero,it is then showed that the Rota-Baxter ideal generated by a polynomial f(x)is the ideal generated by the term of f(x)with the lowest degree;Otherwise,the Rota-Baxter ideal generated by f(x)is either the algebra F[x]or the ideal generated by f(x).

关 键 词：多项式代数 罗巴代数 罗巴算子 罗巴理想 

分 类 号：O15[理学—数学]