Noether整环上的复合Groebner基  

Composed Groebner basis over Noetherian domain

作　　者：陈小松[1] 唐胜[1] 

机构地区：[1]中南大学数学科学与计算技术学院,湖南长沙410083

出　　处：《云南大学学报（自然科学版）》2009年第5期433-438,443,共7页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(10771058);湖南省科技计划资助项目(2007FJ3097)

摘　　要：对于Noether整环上n个变元的多项式环中的Groebner基以及m(m≥n)个变元的多项式环中的复合,通过引入S-多项式及合冲条件,证明了当复合与2个不同多项式环上的项序均相容并且是一组由首幂积为幂置换与置换外其余变元幂积的乘积组成的首1多项式时,Groebner基的计算与复合可交换.从而在此条件下,极小Groebner基的计算也与复合可交换.特别地,当m=n时,如果复合是与项序相容的一组首幂积为幂置换的首1多项式,Groebner基的计算与复合可交换.For Groebner basis in n variables and composition in m （m≥n） variables in a polynomial ring over Noetherian domain, it is proved that Groebner basis computation and composition is commutative if composition is compatible with two term orderings on the different polynomial rings and composition is a lists of monic polynomials with its leading powering products is the products of permuted powering and powering products of other remained variables by using S-polynomial and syzygy condition. Therefore, minimal Groebner basis computation is also commutative with composition under this condition. Especially, Groebner basis computation and composition is commutative if composition is compatible with term orderings and composition is a lists of monic polynomials with its leading powering product is a permuted powering when m = n.

关 键 词：Noether整环 复合Groebner基 合冲模 S-多项式 幂置换 

分 类 号：O153.3[理学—数学]