| Title | Groebner Rings and Modules |
| Author(s) | Bruno Buchberger |
| Type | Article in Conference Proceedings |
| Abstract | We sketch an axiomatic approach for the theory of Groebner bases in rings and modules.
A Groebner ring is a ring with three additional operations: a Noetherian ordering, a ring quotient, and an operation called "least common reducible". In an earlier paper (1985) we had introduced axioms for slightly more complicated additional operations and we pose the problem of finding appropriate axioms for the above three operations in order to guarantee that
- a ring satisfying the axioms allow the construction of Groebner bases by considering finitely many least common reducibles and
- the axioms are preserved if one goes from a ring to the polynomial ring over the given ring and to various other rings that can be constructed from the given ring by various constructive functors. |
| Keywords | axiomatic approach to Groebner bases theory, least common reducibles |
| Length | 4 |
| File |
|
| Language | English |
| Pages | 22-25 |
| Year | 2001 |
| Annote | 2001-10-02-A |
| Note | RISC-Linz Report Series No. 01-20 |
| Editor | S. Maruster and B. Buchberger and V. Negru and T. Jebelean |
| Translation |
No |
| Refereed |
Yes |
| Organization |
University of the West Timisoara |
