Solving System of Linear Congruence Equations over some Rings by Decompositions of Modules
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...
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Kharazmi University
2018-12-01
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| Series: | پژوهشهای ریاضی |
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| Online Access: | http://mmr.khu.ac.ir/article-1-2617-en.html |
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| author | Mahmood Behboodi1 Shadi Asgari Ali Moradzadeh-Dehkordi Amir Hashemi1 |
| author_facet | Mahmood Behboodi1 Shadi Asgari Ali Moradzadeh-Dehkordi Amir Hashemi1 |
| author_sort | Mahmood Behboodi1 |
| collection | DOAJ |
| description | 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 |
| first_indexed | 2024-04-10T00:47:32Z |
| format | Article |
| id | doaj.art-b39ca03cd2304dab88605af92ccf173c |
| institution | Directory Open Access Journal |
| issn | 2588-2546 2588-2554 |
| language | fas |
| last_indexed | 2024-04-10T00:47:32Z |
| publishDate | 2018-12-01 |
| publisher | Kharazmi University |
| record_format | Article |
| series | پژوهشهای ریاضی |
| spelling | doaj.art-b39ca03cd2304dab88605af92ccf173c2023-03-13T19:19:20ZfasKharazmi Universityپژوهشهای ریاضی2588-25462588-25542018-12-0142133152Solving System of Linear Congruence Equations over some Rings by Decompositions of ModulesMahmood Behboodi10Shadi Asgari1Ali Moradzadeh-Dehkordi2Amir Hashemi13 Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran Faculty of Basic Sciences, University of Shahreza, Isfahan, Iran Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran 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.pdfhttp://mmr.khu.ac.ir/article-1-2617-en.htmllinear congruence systemsmodular gaussian eliminationgröbner bases. |
| spellingShingle | Mahmood Behboodi1 Shadi Asgari Ali Moradzadeh-Dehkordi Amir Hashemi1 Solving System of Linear Congruence Equations over some Rings by Decompositions of Modules پژوهشهای ریاضی linear congruence systems modular gaussian elimination gröbner bases. |
| title | Solving System of Linear Congruence Equations over some Rings by Decompositions of Modules |
| title_full | Solving System of Linear Congruence Equations over some Rings by Decompositions of Modules |
| title_fullStr | Solving System of Linear Congruence Equations over some Rings by Decompositions of Modules |
| title_full_unstemmed | Solving System of Linear Congruence Equations over some Rings by Decompositions of Modules |
| title_short | Solving System of Linear Congruence Equations over some Rings by Decompositions of Modules |
| title_sort | solving system of linear congruence equations over some rings by decompositions of modules |
| topic | linear congruence systems modular gaussian elimination gröbner bases. |
| url | http://mmr.khu.ac.ir/article-1-2617-en.html |
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