期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2005
卷号：2005
DOI：10.1155/IJMMS.2005.925
出版社：Hindawi Publishing Corporation
摘要：Let S={x1,x2,…,xn} be a set of positive
integers, and let f be an arithmetical function. The
matrices (S)f=[f(gcd(xi,xj))] and [S]f=[f(lcm [xi,xj])]
are referred to as the greatest common
divisor (GCD) and the least common multiple (LCM) matrices on
S with respect to f, respectively. In this paper, we
assume that the elements of the matrices (S)f and [S]f are integers and study the divisibility of GCD and
LCM matrices and their unitary analogues in the ring Mn(ℤ) of the n×n matrices over the integers.
