|Title||Two-sided Gröbner bases in iterated Ore extensions|
|Author(s)|| Michael Pesch|
|Type||Technical Report, Misc|
|Abstract||We show, how Gröbner bases can be computed for two-sided ideals of iterated Ore extensions with commuting variables. Given a ring R consider an iterated Ore extension with commuting variables.|
Identifying the iterated Ore extension of R and the polynomial ring over R (in the same number of variables) as free left R-Modules all two-sided ideals of the iterated Ore extension are left ideals of the polynomial ring. We therefore define a Gröbner basis of a two-sided ideal of the iterated Ore extension as a Gröbner basis of this two-sided ideal seen as a left ideal of the corresponding polynomial ring. This, of course, requires that left Gröbner bases exist in the polynomial ring. If there is an algorithm for computing a left Gröbner basis for any given finite subset of the polynomial ring this algorithm can be extended to compute two-sided Gröbner bases in the iterated Ore extension. Examples of ground rings R meeting this requirement are polynomial rings over fields or over PID's and solvable polynomial rings.
Fakultät für Mathematik und Informatik (Universität Passau)|