GCD Matrices Defined on GCD-Closed Sets in Principal Ideal Domains

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dc.contributor.author Habre, S. S. en_US
dc.contributor.author El-Kassar, A. N. en_US
dc.contributor.author Awad, Y. A. en_US
dc.date.accessioned 2015-09-15T06:10:46Z en_US
dc.date.available 2015-09-15T06:10:46Z en_US
dc.date.copyright 2010 en_US
dc.date.issued 2015-09-15
dc.identifier.issn 1311-1728 en_US
dc.identifier.uri http://hdl.handle.net/10725/2148 en_US
dc.description.abstract Let S = {x1, x2, ..., xn} be a set of n distinct positive integers. The matrix [S] = (sij) having the greatest common divisor (xi, xj) of xi and xj as its i, j-entry is called the greatest common divisor (GCD) matrix on S. Beslin and Ligh obtained a structure theorem for GCD matrices and generalized Smith’s determinant to factor-closed sets and gcd-closed sets. In a previous paper, we extended many of the results concerning the GCD matrices defined on factorclosed sets to principal ideal domains such as the domain of Gaussian integers and the rings of polynomials over the finite field. In this paper, we extend these results to GCD matrices defined on gcd-closed sets in a principal ideal domain. en_US
dc.language.iso en en_US
dc.title GCD Matrices Defined on GCD-Closed Sets in Principal Ideal Domains en_US
dc.type Article en_US
dc.description.version Published en_US
dc.author.school SOB en_US
dc.author.school SAS en_US
dc.author.idnumber 199329050 en_US
dc.author.idnumber 199529190 en_US
dc.author.woa N/A en_US
dc.author.department Mathematics en_US
dc.description.embargo N/A en_US
dc.relation.journal International Journal of Applied Mathematics en_US
dc.journal.volume 23 en_US
dc.journal.issue 4 en_US
dc.article.pages 571-581 en_US
dc.keywords GCD matrix en_US
dc.keywords GCD-closed set en_US
dc.keywords Principal ideal domain en_US
dc.identifier.doi https://doi.org/10.3844/jmssp.2009.342.347 en_US
dc.identifier.ctation Habre, S. S., Awad, Y. A., El-Kassar, A. N. (2010). GCD Matrices Defined on GCD-Closed Sets in Principal Ideal Domains. International Journal of Applied Mathematics, 23(4), 571-581. en_US
dc.author.email shabre@lau.edu.lb en_US
dc.author.email abdulnasser.kassar@lau.edu.lb en_US
dc.identifier.url https://www.researchgate.net/publication/267672926_GCD_matrices_defined_on_GCD-closed_sets_in_a_PID en_US
dc.orcid.id https://orcid.org/0000-0002-8423-8723 en_US

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