Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584940 | Journal of Algebra | 2014 | 25 Pages |
Abstract
As an application, we consider the signed generating series, denoted by NM(n,R)Ã,deg(t) and called the skew-growth function, of least common multiples of all finite sets of irreducible elements of M(n,R)Ã, assuming R is residue finite. Then, using the above divisibility theory, we show the Euler product decomposition of the skew-growth function:NM(n,R)Ã,deg(exp(âs))=âpâ{primesofR}(1âN(p)âs)(1âN(p)âs+1)â¯(1âN(p)âs+nâ1) Here N(p):=#(R/(p)) is the absolute norm of pâR (there is an unfortunate coincidence of notation “N” for the absolute norm and for the skew growth function [6]).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Kyoji Saito,