首页|Linear Diophantine equations in several variables
Linear Diophantine equations in several variables
扫码查看
点击上方二维码区域，可以放大扫码查看
原文链接
NSTL
Elsevier
Let R be a ring and let (a(1), . . . , a(n)). Rnbe a unimodular vector, where n >= 2 and each a(i) is in the center of R. Consider the linear equation a(1)X(1)+ . . . + a(n)X(n) = 0, with solution set S. Then S = S-1+ . . . + S-n, where each S-i is naturally derived from (a(1), . . . , a(n)), and we give a presentation of Sin terms of generators taken from the S-i and appropriate relations. Moreover, under suitable assumptions, we elucidate the structure of each quotient module S/S-i. Furthermore, assuming that R is a principal ideal domain, we provide a simple way to construct a basis of Sand, as an application, we determine the structure of the quotient module S/U-i, where each U-i is a specific module containing S-i. (C) 2021 Elsevier Inc. All rights reserved.
Linear Diophantine equationUnimodular vectorSmith normal formSYSTEMS
NSTL
Elsevier
