Intersection of Ideals in a Polynomial Ring over a Dual Valuation Domain
Let V be a valuation domain and let A=V+εV be a dual valuation domain. We propose a method for computing a strong Gröbner basis in R=A[x1,…,xn]; given polynomials f1,…,fs∈R, a method for computing a generating set for Syz(f1,…,fs)={(h1,…,hs)∈Rs∣h1f1+⋯+hsfs=0} is given; and, finally, given two ideals...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2018/9316901 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832561265284743168 |
|---|---|
| author | Regis F. Babindamana Andre S. E. Mialebama Bouesso |
| author_facet | Regis F. Babindamana Andre S. E. Mialebama Bouesso |
| author_sort | Regis F. Babindamana |
| collection | DOAJ |
| description | Let V be a valuation domain and let A=V+εV be a dual valuation domain. We propose a method for computing a strong Gröbner basis in R=A[x1,…,xn]; given polynomials f1,…,fs∈R, a method for computing a generating set for Syz(f1,…,fs)={(h1,…,hs)∈Rs∣h1f1+⋯+hsfs=0} is given; and, finally, given two ideals I=〈f1,…,fs〉 and J=〈g1,…,gr〉 of R, we propose an algorithm for computing a generating set for I∩J. |
| format | Article |
| id | doaj-art-0ba3c9e1fdd0473ebdd8b9c01710120e |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-0ba3c9e1fdd0473ebdd8b9c01710120e2025-02-03T01:25:27ZengWileyJournal of Mathematics2314-46292314-47852018-01-01201810.1155/2018/93169019316901Intersection of Ideals in a Polynomial Ring over a Dual Valuation DomainRegis F. Babindamana0Andre S. E. Mialebama Bouesso1Université Marien Ngouabi, Faculté des Sciences et Technique Département de Mathématiques, BP: 69, Brazzaville, CongoUniversité Marien Ngouabi, Faculté des Sciences et Technique Département de Mathématiques, BP: 69, Brazzaville, CongoLet V be a valuation domain and let A=V+εV be a dual valuation domain. We propose a method for computing a strong Gröbner basis in R=A[x1,…,xn]; given polynomials f1,…,fs∈R, a method for computing a generating set for Syz(f1,…,fs)={(h1,…,hs)∈Rs∣h1f1+⋯+hsfs=0} is given; and, finally, given two ideals I=〈f1,…,fs〉 and J=〈g1,…,gr〉 of R, we propose an algorithm for computing a generating set for I∩J.http://dx.doi.org/10.1155/2018/9316901 |
| spellingShingle | Regis F. Babindamana Andre S. E. Mialebama Bouesso Intersection of Ideals in a Polynomial Ring over a Dual Valuation Domain Journal of Mathematics |
| title | Intersection of Ideals in a Polynomial Ring over a Dual Valuation Domain |
| title_full | Intersection of Ideals in a Polynomial Ring over a Dual Valuation Domain |
| title_fullStr | Intersection of Ideals in a Polynomial Ring over a Dual Valuation Domain |
| title_full_unstemmed | Intersection of Ideals in a Polynomial Ring over a Dual Valuation Domain |
| title_short | Intersection of Ideals in a Polynomial Ring over a Dual Valuation Domain |
| title_sort | intersection of ideals in a polynomial ring over a dual valuation domain |
| url | http://dx.doi.org/10.1155/2018/9316901 |
| work_keys_str_mv | AT regisfbabindamana intersectionofidealsinapolynomialringoveradualvaluationdomain AT andresemialebamabouesso intersectionofidealsinapolynomialringoveradualvaluationdomain |