Solving System of Linear Congruence Equations over some Rings by Decompositions of Modules

Behboodi1, Mahmood; Asgari, Shadi; Moradzadeh-Dehkordi, Ali; Hashemi1, Amir

doi:10.29252/mmr.4.2.133

Volume 4, Issue 2 (Vol. 4, No. 2 2018) mmr 2018, 4(2): 133-152 | Back to browse issues page

‎ 10.29252/mmr.4.2.133

‎ 20.1001.1.25882546.1397.4.2.3.0

Mendeley

Zotero

RefWorks

Behboodi1 M, Asgari S, Moradzadeh-Dehkordi A, Hashemi1 A. Solving System of Linear Congruence Equations over some Rings by Decompositions of Modules. mmr 2018; 4 (2) :133-152
URL: http://mmr.khu.ac.ir/article-1-2617-en.html

Solving System of Linear Congruence Equations over some Rings by Decompositions of Modules

Mahmood Behboodi1¹

, Shadi Asgari²

, Ali Moradzadeh-Dehkordi³

, Amir Hashemi1

⁴

1- Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran
2- School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
3- Faculty of Basic Sciences, University of Shahreza, Isfahan, Iran
4- Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran , amir.hashemi@ipm.ir

Abstract: (2888 Views)

In this paper, we deal with solving systems of linear congruences over commutative CF-rings. More precisely, let R be a CF-ring (every finitely generated direct sum of cyclic R-modules has a canonical form) and let I_1,..., I_n be n ideals of R. We introduce congruence matrices theory techniques and exploit its application to solve the above system. Further, we investigate the application of computer algebra techniques (Gröbner bases) in this context whenever R = Z../files/site1/files/42/2Abstract.pdf

Keywords: Linear congruence systems, Modular Gaussian elimination, Gröbner bases.

Full-Text [PDF 949 kb] (682 Downloads)