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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| Format: | Article |
| Language: | English |
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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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| author | Pentti Haukkanen Ismo Korkee |
| author_facet | Pentti Haukkanen Ismo Korkee |
| author_sort | Pentti Haukkanen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3f0397189d7b40c5b2d5fb6ab19a39d3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3f0397189d7b40c5b2d5fb6ab19a39d32025-02-03T05:48:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005692593510.1155/IJMMS.2005.925Notes on the divisibility of GCD and LCM MatricesPentti Haukkanen0Ismo Korkee1Department of Mathematics, Statistics and Philosophy, University of Tampere, Tampere 33014, FinlandDepartment of Mathematics, Statistics and Philosophy, University of Tampere, Tampere 33014, FinlandLet 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.http://dx.doi.org/10.1155/IJMMS.2005.925 |
| spellingShingle | Pentti Haukkanen Ismo Korkee Notes on the divisibility of GCD and LCM Matrices International Journal of Mathematics and Mathematical Sciences |
| title | Notes on the divisibility of GCD and LCM Matrices |
| title_full | Notes on the divisibility of GCD and LCM Matrices |
| title_fullStr | Notes on the divisibility of GCD and LCM Matrices |
| title_full_unstemmed | Notes on the divisibility of GCD and LCM Matrices |
| title_short | Notes on the divisibility of GCD and LCM Matrices |
| title_sort | notes on the divisibility of gcd and lcm matrices |
| url | http://dx.doi.org/10.1155/IJMMS.2005.925 |
| work_keys_str_mv | AT penttihaukkanen notesonthedivisibilityofgcdandlcmmatrices AT ismokorkee notesonthedivisibilityofgcdandlcmmatrices |