On GCED matrices over UFDs-Reference-Cited by-同舟云学术

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On GCED matrices over UFDs

Published:2022 Issue:11 Volume:36 Page:3775-3784
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Zeid W.¹,Chehade H.¹,Rasheed F.²

Affiliation:

1. Department of Mathematics and Physics, School of Arts and Sciences, The International University of Beirut, Saida, Lebanon

2. Department of Mathematics and Physics, School of Arts and Sciences, Lebanese International University, Saida, Lebanon

Abstract

An extension of the GCED matrices from the domain of natural integers to the unique factorization domain is given. The structure of these type of matrices defined on both arbitrary sets and GCED-closed sets are presented. Moreover, we present exact expressions for the determinant and the inverse of such matrices. The domains of Gaussian integers and polynomials over finite fields are used to illustrate the work.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference15 articles.

1. Y. Awad, H. Chehade, R. Mghames, Reciprocal Power GCDQ Matrices and Power LCMQ Matrices Defined on Factor Closed Sets over Euclidean Domains, Filomat 34 (2020) 357-363.

2. S. Beslin, A. El-Kassar, GCD matrices and Smith’s determinant Over U.F.D., Bull. Number Theory Related Topics 13 (1989) 17-22.

3. S. Beslin, S. Ligh, Greatest common divisor matrices. Linear Algebra Appl. 118 (1989) 69-76.

4. S. Beslin, S. Ligh, Another generalization of Smith’s determinant of GCD matrices, Fibonacci Quart. 30 (1992) 157-160.

5. S. Chun, GCD and LCM Power Matrices, AMS (1996) 290-297.

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