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Power GCD Matrices for a UFD.
- Source :
-
Algebra Colloquium . Mar2009, Vol. 16 Issue 1, p71-78. 8p. - Publication Year :
- 2009
-
Abstract
- Let S = {x1,..., xn} be a set of n distinct positive integers and e ≥ 1 an integer. Then we call the n × n matrix (Se) = ((xi, xj)e) having the eth power of the greatest common divisor (xi, xj) of xi and xj as its (i, j)-entry the power greatest common divisor (GCD) matrix on S. A well-known formula for det(Se) when S = {1, ..., n} was given by H.J.S. Smith in 1875/76. In this paper, we consider the power GCD matrices for a UFD along the direction of their structure, determinant and non-singularity, and consequently, we extend the classical result of Smith as well as the results of Beslin and Kassar on UFD given in 1989. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MATRICES (Mathematics)
*ALGEBRA
*MATHEMATICS
*RINGS of integers
*DIVISOR theory
Subjects
Details
- Language :
- English
- ISSN :
- 10053867
- Volume :
- 16
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Algebra Colloquium
- Publication Type :
- Academic Journal
- Accession number :
- 35884226
- Full Text :
- https://doi.org/10.1142/S100538670900008X