四川大学学报（自然科学版）2012，Vol.49Issue(2)：253-257,5.DOI:10.3969/j.issn.0490-6756.2012.02.001
定义在三个互素因子链上的交错幂GCD和交错幂LCM矩阵的整除性
Divisibility of alternating Smith matrices on three coprime divisor chains
摘要
Abstract
Let S = {χ1.χ2, …χXx,} be a set of n distinct positive integers and a ≥ 1 be an integer. The matrix ((-1I)I+j(χi,χj)a) having the a th power (-1)I+j (χ,χj)a as its (I,j) -entry is called a th power-alternating greatest common divisor (GCD) matrix defined on S , abbreviated by (Asa). Similarly we can define the a th power alternating LCM matrix ((-1)I+j [χi,χj]a), abbreviated by [Asa]. In this paper, we assume that S consists of two coprime divisor chains and ∈S. We show the following results are true. IF a|6, then det(Asa) | det(Asb) ,det[Asa] | det [Asb],det( Asa) I det [Asb]; lt a\b, then in the ringMn (Z) of n X n matrices over the integers, we have (Asa) | (Asb), [Asa]| [Asb], (Asa) | [Asb]. But such results fail to be true if a/b.关键词
整除/三个互素因子链/交错幂GCD矩阵/交错幂LCM矩阵Key words
divisibility, three coprime divisor chains, alternating power GCD matrix, alternating power LCM matrix分类
数理科学引用本文复制引用
李懋,谭千蓉..定义在三个互素因子链上的交错幂GCD和交错幂LCM矩阵的整除性[J].四川大学学报（自然科学版）,2012,49(2):253-257,5.基金项目
中央高校基本科研业务费专项资金资助(XDJK2010C058) （XDJK2010C058）
高等学校博士学科点专项科研基金(20100181110073) （20100181110073）
