On Unitary Analogs of GCD Reciprocal LCM Matrices
Yükleniyor...
Dosyalar
Tarih
2010
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Taylor & Francis Ltd
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
A divisor d is an element of Z(+) of n is an element of Z(+) is said to be a unitary divisor of n if (d, n/d)=1. In this article we examine the greatest common unitary divisor (GCUD) reciprocal least common unitary multiple (LCUM) matrices. At first we concentrate on the difficulty of the non-existence of the LCUM and we present three different ways to overcome this difficulty. After that we calculate the determinant of the three GCUD reciprocal LCUM matrices with respect to certain types of functions arising from the LCUM problematics. We also analyse these classes of functions, which may be referred to as unitary analogs of the class of semimultiplicative functions, and find their connections to rational arithmetical functions. Our study shows that it does make a difference how to extend the concept of LCUM.
Açıklama
Anahtar Kelimeler
GCD matrix, LCM matrix, unitary divisor meet semilattice, semimultiplicative function, rational arithmetical function
Kaynak
Linear & Multilinear Algebra
WoS Q Değeri
Q2
Scopus Q Değeri
Q2
Cilt
58
Sayı
5
Künye
Haukkanen, P., lmonen, P., Nallı, A., Sillanpaa, J., (2010). On Unitary Analogs of GCD Reciprocal LCM Matrices. Linear & Multilinear Algebra, 58(5), 599-616. Doi: 10.1080/03081080902816576
