Details:
Title  Twosided Gröbner bases in iterated Ore extensions  Author(s)  Michael Pesch  Type  Technical Report, Misc  Abstract  We show, how Gröbner bases can be computed for twosided 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 RModules all twosided ideals of the iterated Ore extension are left ideals of the polynomial ring. We therefore define a Gröbner basis of a twosided ideal of the iterated Ore extension as a Gröbner basis of this twosided 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 twosided 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.  Length  19 
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 Language  English  Number  MIP9602  Year  1996  Month  February  Edition  0  Translation 
No  Refereed 
No  Organization 
Universität Passau  Institution 
Fakultät für Mathematik und Informatik (Universität Passau) 
