Notes on the divisibility of GCD and LCM Matrices
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,...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.925 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |