|Title||Effective Gröbner Structures|
|Author(s)|| Joachim Apel|
|Type||Technical Report, Misc|
|Abstract||Since Buchberger introduced the theory of Groebner bases in 1965 it has become one of the most important tools in constructive algebra and, nowadays, it is the kernel of many algorithms in the theory of polynomial ideals and algebraic geometry. Motivated by the results in polynomial|
rings there have been investigated a lot of possibilities to generalise Buchberger's ideas to other types of rings. The perhaps most general concept, though it does not cover all extensions reported in the literature, is the extension to graded structures due to Robbiano and Mora. But in order to obtain algorithmic solutions for the computation of Grobner bases it needs additional computability assumptions. The subject of this paper is the presentation of some classes of effective graded structures.