论文标题
通过扩展Gröbner-Shirshov基地来构建自由差分代数
Construction of free differential algebras by extending Gröbner-Shirshov bases
论文作者
论文摘要
作为一个基本概念，集合上的自由差异代数被构造为差异变量上的多项式代数。这种构造因从差分代数到代数而不是集合而不是集合而不是集合的左伴随函数，而不是集合，这种结构以代数上的自由差分代数的更一般概念而闻名。在本文中，我们表明，基本代数的发电机 - 连接属性可以扩展到该基本代数上的自由差分代数。更确切地说，基本代数的gröbner-Shirshov基础特性可以扩展到该基本代数的自由差分代数，从而使这些更一般的自由差异代数的Poincaré-Birkhoff-Witt类型基础。给出示例作为插图。
As a fundamental notion, the free differential algebra on a set is concretely constructed as the polynomial algebra on the differential variables. Such a construction is not known for the more general notion of the free differential algebra on an algebra, from the left adjoint functor of the forgetful functor from differential algebras to algebras, instead of sets. In this paper we show that generator-relation properties of a base algebra can be extended to the free differential algebra on this base algebra. More precisely, a Gröbner-Shirshov basis property of the base algebra can be extended to the free differential algebra on this base algebra, allowing a Poincaré-Birkhoff-Witt type basis for these more general free differential algebras. Examples are given as illustrations.
