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Greatest common divisor and least common multiple matrices on factor closed sets in a principal ideal domain

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dc.contributor.author El-Kassar, A. N.
dc.contributor.author Habre, S. S.
dc.contributor.author Awad, Y. A.
dc.date.accessioned 2016-12-08T07:43:40Z
dc.date.available 2016-12-08T07:43:40Z
dc.date.copyright 2009 en_US
dc.identifier.issn 1549-3644 en_US
dc.identifier.uri http://hdl.handle.net/10725/4894
dc.description.abstract Let T be a set of n distinct positive integers, x1, x2, ..., xn. The n×n matrix [T] having (xi , xj), the greatest common divisor of xi and xj , as its (i,j)-entry is called the greatest common divisor (GCD) matrix on T. The matrix [[T]] whose (i,j)-entry is [xi , xj], the least common multiple of xi and xj , is called the least common multiple (LCM) matrix on T. Many aspects of arithmetics in the domain of natural integers can be carried out to Principal Ideal Domains (PID). In this study, we extend many recent results concerning GCD and LCM matrices defined on Factor Closed (FC) sets to an arbitrary PID such as the domain of Gaussian integers and the ring of polynomials over a finite field. Approach: In order to extend the various results, we modified the underlying computational procedures and number theoretic functions to the arbitrary PIDs. Properties of the modified functions and procedures were given in the new settings. Results: Modifications were used to extend the major results concerning GCD and LCM matrices defined on FC sets in PIDs. Examples in the domains of Gaussian integers and the ring of polynomials over a finite field were given to illustrate the new results. Conclusion: The extension of the GCD and LCM matrices to PIDs provided a lager class for such matrices. Many of the open problems can be investigated in the new settings. en_US
dc.language.iso en en_US
dc.title Greatest common divisor and least common multiple matrices on factor closed sets in a principal ideal domain en_US
dc.type Article en_US
dc.description.version Published en_US
dc.author.school SOB en_US
dc.author.idnumber 199529190 en_US
dc.author.idnumber 199329050 en_US
dc.author.department Department of Information Technology and Operations Management (ITOM) en_US
dc.description.embargo N/A en_US
dc.relation.journal Journal of Mathematics and Statistics en_US
dc.journal.volume 5 en_US
dc.journal.issue 4 en_US
dc.article.pages 342-347 en_US
dc.keywords GCD matrix en_US
dc.keywords Lcm matrix en_US
dc.keywords Factor-closed sets en_US
dc.keywords Principal ideal domain en_US
dc.identifier.doi http://dx.doi.org/10.3844/jmssp.2009.342.347 · Source: DOAJ en_US
dc.identifier.ctation El-Kassar,A.N., Habre, S.S., Awad, Y.A. (2009). Greatest common divisor and least cmmon multiple matrices on factor closed sets in a principal ideal domain:.Journal od mathematics and statistics, 5(4), 342-347 en_US
dc.author.email abdulnassar.kassar@lau.edu.lb en_US
dc.author.email shabre@lau.edu.lb en_US
dc.identifier.tou http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php en_US
dc.identifier.url https://www.researchgate.net/publication/41025275_Greatest_Common_Divisor_and_Least_Common_Multiple_Matrices_on_Factor_Closed_Sets_in_a_Principal_Ideal_Domain en_US
dc.orcid.id https://orcid.org/0000-0002-8423-8723
dc.orcid.id https://orcid.org/0000-0002-7887-8767
dc.author.affiliation Lebanese American University en_US


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