论文标题
一个变量中多项式环的对称多项式和外部功率
Symmetric polynomials and exterior power of a polynomial ring in one variable
论文作者
论文摘要
在本文中，我们考虑了一个变量中多项式环的外部功率和对称张量。该多项式环的联想半段代数的结构诱导了对称的张量，其结构是关联的半元代数的结构，而外部功率在对称量量的半族代数上诱导半族模块的结构。对称多项式的代数是一个变量中多项式环的对称张量的代数同构。我们通过基本对称的多项式获得了对称多项式的显式表达，并通过基本对称的多项式多项式元素和下层多项式程度的外部力量的元素来获得外部功率元素的显式表达。
In this article we consider the exterior power and the symmetric tensors of the polynomial ring in one variable. The structure of an associative semigraded algebra of this polynomial ring induces on the symmetric tensors the structure of an associative semigraded algebra, and on the exterior power induces structure of a semigraded module over semigraded algebra of symmetric tensors. The algebra of symmetric polynomials is isomorphic to the algebra of the symmetric tensors of polynomial ring in one variables. We obtained the explicit expression for symmetric polynomials via elementary symmetric polynomials and the explicit expression for elements of the exterior power via elementary symmetric polynomials and elements of the exterior power of the lower polynomial degree.
