多项式代数上的罗巴理想

Rota-Baxter Ideals on Polynomial Algebras

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).