W-Grbner basis and monomial ideals under polynomial composition  

作　　者：LI Dong-mei LIU Jin-wang LIU Wei-jun 

机构地区：[1]School of Mathematical Sciences and Computing Technology, Central South University, Changsha410075, China [2]School of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2011年第3期287-294,共8页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the NSFC (10771058, 11071062, 10871205), NSFH (10JJ3065);Scientific Research Fund of Hunan Provincial Education Department (10A033);Hunan Provincial Degree and Education of Graduate Student Foundation (JG2009A017)

摘　　要：The notion of weakly relatively prime and W-Gr6bner basis in K[x1, x2,…, xn] are given. The following results are obtained： for polynomials fl, f2, ..., fm, {f1^λ1, f2^λ2,…, fm^λm} is a GrSbner basis if and only if f1, f2, …, fm are pairwise weakly relatively prime with λ1, λ2, …, λm arbitrary non-negative integers; polynomial composition by θ = （θ1,θ2, …, θn） commutes with monomial-Grobner bases computation if and only if θ1, θ2, , θm are pairwise weakly relatively prime.The notion of weakly relatively prime and W-Gr6bner basis in K[x1, x2,…, xn] are given. The following results are obtained： for polynomials fl, f2, ..., fm, {f1^λ1, f2^λ2,…, fm^λm} is a GrSbner basis if and only if f1, f2, …, fm are pairwise weakly relatively prime with λ1, λ2, …, λm arbitrary non-negative integers; polynomial composition by θ = （θ1,θ2, …, θn） commutes with monomial-Grobner bases computation if and only if θ1, θ2, , θm are pairwise weakly relatively prime.

关 键 词：W-Grobner basis weakly relatively prime polynomial composition. 

分 类 号：O174.14[理学—数学] O153.3[理学—基础数学]