多元多项式环上模的中国剩余定理  

Chinese remainder theorem of modules over multivariate polynomial rings

作　　者：刘金旺[1] 吴弢 李冬梅[1] Liu Jinwang;Wu Tao;Li Dongmei

机构地区：[1]湖南科技大学数学与计算科学学院,湘潭411201

出　　处：《中国科学：数学》2022年第9期989-996,共8页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11971161和11871207)资助项目。

摘　　要：中国剩余定理在数论及代数中起着重要的作用.在多元多项式环中,中国剩余定理可以转化为多元多项式同余方程组的求解,借助代数理论,可以找到满足同余方程组的多项式.本文研究多元多项式环上关于模的中国剩余定理,并利用模的Grobner基理论与方法找出满足模的中国剩余定理的多项式向量,从而找到多项式环上模的同余方程组的解.The Chinese remainder theorem plays an important role in the areas of number theory and algebra.In the multivariate polynomial rings,the Chinese remainder theorem can be used to solve systems of multivariate polynomial congruence equations.With the help of algebra theory,polynomials that satisfy the congruence equations can be found.In this paper,we investigate the Chinese remainder theorem of modules over multivariate polynomial rings.Using the theory and method of Grobner bases for modules,we find the polynomial vector that satisfies the Chinese remainder theorem of modules.Furthermore,we obtain the solutions of systems of congruence equations for modules over polynomial rings.

关 键 词：中国剩余定理 模的Grobner基 模的交 同余方程组 

分 类 号：O174.14[理学—数学] O153.3[理学—基础数学]