Power GCD Matrices for a UFD

DOI10.1142/S100538670900008XzbMath1247.11033OpenAlexW2005696937MaRDI QIDQ3607455

Xingwang Zhou, Jianrong Zhao, Shao-Fang Hong

Publication date: 2 March 2009

Published in: Algebra Colloquium (Search for Journal in Brave)

Full work available at URL: http://www.worldscinet.com/ac/16/1601/S100538670900008X.html

zbMATH Keywords

UFDfactor-closed (FC) setpower GCD P-matricesprime residue system

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Matrices of integers (15B36) Matrices, determinants in number theory (11C20)

Related Items (11)

Determinants of Smith matrices on three coprime divisor chains and divisibility ⋮ On a certain determinant for a U.F.D. ⋮ LU-FACTORIZATIONS OF SYMMETRIC MATRICES WITH APPLICATIONS ⋮ Multiple divisor chains and determinants of matrices associated with completely even functions (modr) ⋮ Divisibility of determinants of power GCD matrices and power LCM matrices on finitely many quasi-coprime divisor chains ⋮ Upper bounds for the condition numbers of the GCD and the reciprocal GCD matrices in spectral norm ⋮ Determinants and divisibility of power GCD and power LCM matrices on finitely many coprime divisor chains ⋮ Divisibility among power GCD matrices and among power LCM matrices on three coprime divisor chains ⋮ Reciprocal power GCDQ matrices and power LCMQ matrices defined on factor closed sets over Euclidean domains ⋮ Some properties of row-adjusted meet and join matrices ⋮ A topological approach to divisibility of arithmetical functions and GCD matrices

Cites Work

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• ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF GREATEST COMMON DIVISOR MATRICES
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• On a general form of meet matrices associated with incidence functions
• Diophantine Approximations and Hilbert's Space

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