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...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2018-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2018/9316901 |
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doaj-0ba3c9e1fdd0473ebdd8b9c01710120e2020-11-25T00:58:55ZengHindawi LimitedJournal 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Regis F. Babindamana Andre S. E. Mialebama Bouesso |
| spellingShingle |
Regis F. Babindamana Andre S. E. Mialebama Bouesso Intersection of Ideals in a Polynomial Ring over a Dual Valuation Domain Journal of Mathematics |
| author_facet |
Regis F. Babindamana Andre S. E. Mialebama Bouesso |
| author_sort |
Regis F. Babindamana |
| title |
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_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_sort |
intersection of ideals in a polynomial ring over a dual valuation domain |
| publisher |
Hindawi Limited |
| series |
Journal of Mathematics |
| issn |
2314-4629 2314-4785 |
| publishDate |
2018-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2018/9316901 |
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AT regisfbabindamana intersectionofidealsinapolynomialringoveradualvaluationdomain AT andresemialebamabouesso intersectionofidealsinapolynomialringoveradualvaluationdomain |
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