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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2018-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2018/9316901 |
| Summary: | 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. |
|---|---|
| ISSN: | 2314-4629 2314-4785 |