四川大学学报（自然科学版）2008，Vol.45Issue(3)：485-487,3.
使得幂GCD阵(Se)整除幂LCM矩阵[Se]的四元gcd封闭集S的一个刻画
A characterization of the gcd-closed set S with |S|=4such that (Se) divides [Se]
摘要
Abstract
In 2002, Hong showed that for any gcd-closed set S with |S|≤3,the GCD matrix (S) on S divides the LCM matrix [S] on S in the ring M|S|(Z) of |S|×|S| matrices over the integers. Let e≥1 be an arbitrary given integer. In this paper, a necessary and sufficient conditions on the gcd closed set S with |S|=4 such that the power GCD matrix (Se)on S divides the power LCM matrix [Se] on S in the ring M4(Z) of 4×4 matrices over the integers is proved. This solves partially an open question raised by Hong in 2002.关键词
幂GCD矩阵/幂LCM矩阵/gcd封闭集/整除性Key words
power GCD matrix,power LCM matrix,gcd-closed set,divisibility分类
数理科学引用本文复制引用
赵建容..使得幂GCD阵(Se)整除幂LCM矩阵[Se]的四元gcd封闭集S的一个刻画[J].四川大学学报（自然科学版）,2008,45(3):485-487,3.基金项目
教育部"新世纪优秀人才支持计划"(NCET-06-0785) （NCET-06-0785）
