Details:
Title  Gr\"obner bases for ideals of $sigma$PBW extensions.  Author(s)  Claudia Gallego, Oswaldo Lezama  Type  Article in Journal  Abstract  In this article, we introduce the σPWB extensions and construct the theory of Gröbner bases for the left ideals of them. We prove the Hilbert's basis theorem and the division algorithm for this more general class of Poincaré–Birkhoff–Witt extensions. For the particular case of bijective and quasicommutative σPWB extensions, we implement the Buchberger's algorithm for computing Gröbner bases of left ideals.  Keywords  Buchberger's algorithm, Noetherian polynomial noncommutative rings, Noncommutative Gröbner bases, PBW extensions,  ISSN  00927872; 15324125/e 
URL 
http://www.tandfonline.com/doi/abs/10.1080/00927870903431209 
Language  English  Journal  Commun. Algebra  Volume  39  Number  1  Pages  5075  Publisher  Taylor & Francis, Philadelphia, PA  Year  2011  Edition  0  Translation 
No  Refereed 
No 
