ON THE DIVISIBILITY AMONG POWER LCM MATRICES ON GCD-CLOSED SETS

DOI10.1017/S0004972722000491WikidataQ114117685 ScholiaQ114117685MaRDI QIDQ5879210

Guangyan Zhu, Mao Li

Publication date: 28 February 2023

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

divisibilitypower LCM matrixgreatest-type divisor\(\gcd\)-closed set

Mathematics Subject Classification ID

Matrices of integers (15B36) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Matrices, determinants in number theory (11C20)

Cites Work

• Non-divisibility of LCM matrices by GCD matrices on \(\gcd\)-closed sets
• On the divisibility of meet and join matrices
• Divisibility properties of power LCM matrices by power GCD matrices on gcd-closed sets
• On GCD and LCM matrices
• On the Bourque-Ligh conjecture of least common multiple matrices
• On the factorization of LCM matrices on gcd-closed sets
• On a certain arithmetical determinant
• Divisibility among power GCD matrices and among power LCM matrices on finitely many coprime divisor chains
• GCD-closed sets and divisibility of Smith matrices
• Divisibility properties of power GCD matrices and power LCM matrices
• Generalized LCM matrices
• Another generalisation of smith's determinant
• Matrices associated with arithmetical functions
• Notes on power LCM matrices
• On the divisibility of matrices associated with multiplicative functions
• On the divisibility among power GCD and power LCM matrices on gcd-closed sets
• Divisibility properties of Smith matrices
• Divisibility of power LCM matrices by power GCD matrices on gcd-closed sets

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