| Title | The Membership Problem for finitely generated quadratic modules in the univariate case |
| Author(s) | Doris Augustin |
| Type | Article in Journal |
| Abstract | We prove that the Membership Problem is solvable affirmatively for every finitely generated quadratic module Q of R [ X 1 ] . For the case that the associated semialgebraic set S is bounded we show that a polynomial f is an element of Q if and only if f is nonnegative on S and fulfills certain order conditions in the boundary points of S . This leads us to the definition of generalized natural generators of the quadratic module Q . |
| ISSN | 0022-4049 |
| URL |
http://www.sciencedirect.com/science/article/pii/S0022404912000436 |
| Language | English |
| Journal | Journal of Pure and Applied Algebra |
| Volume | 216 |
| Number | 10 |
| Pages | 2204 - 2212 |
| Year | 2012 |
| Edition | 0 |
| Translation |
No |
| Refereed |
No |
