四川大学学报（自然科学版）2011，Vol.48Issue(6)：1261-1265,5.DOI:10.3969/j.issn.0490-6756.2011.06.007
定义在两个互素因子链上的交错Smith矩阵的整除性
Divisibility of alternating Smith matrices on two coprime divisor chains
摘要
Abstract
Let S = {x1 ,x2, x3 ,xn} be a set of n distinct positive integers and a≥l an integer. The matrix having the ath power (-1)I+j(xi,xj)a as its (I,,j) -entry is called ath power alternating greatest common divisor (GCD) matrix defined on S, denoted by (AS°), where (xi,xj)a = (gcd(xi ,xy))a. Similarly we can define the ath power alternating LCM matrix [Asa]. In this paper, the authors show the following results are true: assume that S consists of two coprime divisor chains and 1 ∈ S, if a |b, then det(Asa) | det(Asb) ,det[Asa] | det [Asb],det(Asa) | det[AS6]; if a | b, then in the ring of n by n matrices over in tegers, (Asa) | (Asb),[Asa] | [Asb],(Asa) | [Asb]; but such results fail to be true if a×b.关键词
整除/因子链/交错幂GCD矩阵/交错幂LCM矩阵Key words
divisbility/divisor chain/power alternating GCD matrix/power alternating LCM matrix分类
数理科学引用本文复制引用
林宗兵,罗淼..定义在两个互素因子链上的交错Smith矩阵的整除性[J].四川大学学报（自然科学版）,2011,48(6):1261-1265,5.基金项目
攀枝花学院计算机学院预研项目(Y2011-04) （Y2011-04）
