کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4603566 1336964 2008 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Divisibility properties of power GCD matrices and power LCM matrices
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Divisibility properties of power GCD matrices and power LCM matrices
چکیده انگلیسی

Let a,b and n be positive integers and the set S={x1,…,xn} of n distinct positive integers be a divisor chain (i.e. there exists a permutation σ on {1,…,n} such that xσ(1)|…|xσ(n)). In this paper, we show that if a|b, then the ath power GCD matrix (Sa) having the ath power (xi,xj)a of the greatest common divisor of xi and xj as its i,j-entry divides the bth power GCD matrix (Sb) in the ring Mn(Z) of n×n matrices over integers. We show also that if a∤b and n⩾2, then the ath power GCD matrix (Sa) does not divide the bth power GCD matrix (Sb) in the ring Mn(Z). Similar results are also established for the power LCM matrices.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 428, Issue 4, 1 February 2008, Pages 1001-1008