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Title  Left and right Gröbner bases in Ore extensions of polynomial rings  Author(s)  Michael Pesch  Type  Technical Report, Misc  Abstract  We show, that Groebner bases can be computed for left and right ideals of certain Ore extensions of polynomial rings.
Consider an Ore extension K[X_1, ... , X_m] [Y; alpha, gamma] of a polynomial ring over a field, where alpha (X_i) = X_i^(l_i) + f_i for some f_i in K[X_1, ... ,Xm], f_i ? X^(l_i)_i for some admissible term order ?, e_i in N ?? 0 ? and alpha  K = id. This rings are in general neither right nor left Noetherian. Nevertheless finite left and right Groebner bases for finitely generated left and right ideals do exist for special term orders. Using this Groebner bases the ideal membership problem can be solved. For other term orders no finite Groebner bases exist in general. Finite left and right Groebner bases can be computed using left/right reduction and spolynomials (based on right/left divisibility and left/right least common multiples) in Buchbergers algorithm. Termination can be proven by a modified Dickson lemma, using the special term order.  Length  32 
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 Language  English  Year  1996  Edition  0  Translation 
No  Refereed 
No 
