微分算子环的强既约Grbner基  

Strong Reduced Grbner Bases in Rings of Differential Operators

作　　者：胡嘉卉[1] 

机构地区：[1]河南工业大学理学院 郑州450052

出　　处：《重庆工学院学报（自然科学版）》2008年第4期58-62,共5页Journal of Chongqing Institute of Technology

基　　金：河南工业大学基金资助项目(07XJC047)

摘　　要：为解决计算微分算子环中Grbner基的Buchberger算法与Insa-Pauer算法在某些情况下不能将Grbner基进一步简化的问题,K.Nabeshima给出了微分算子环的弱既约Grbner基的定义和算法,但弱既约Grbner基并不唯一.为此,给出了微分算子环的强既约Grbner基的定义及算法,并证明微分算子环的强既约Grbner基的存在性和唯一性.In order to solve the problem that in some conditions, Buchberger algorithm and Insa-Pauer algorithm to calculate the Grobner bases in the rings of differential operators can not further simplify Grobner bases, K. Nabeshima presents the definition and algorithm of weak reduced Grobner bases in rings of differential operators, but weak reduced Grobner base is not unique. Therefore, this paper presents the definition and algorithm of strong reduced Grobner bases in rings of differential operators and proves the existence and uniqueness of the strong reduced Grobner bases in rings of differential operators.

关 键 词：微分算子环 强既约Grobner基 弱既约Grobner基 

分 类 号：O153[理学—数学]