Details:
Title  Looking for Gröbner basis theory for (almost) skew 2nomial algebras  Author(s)  Huishi Li  Type  Article in Journal  Abstract  In this paper, we introduce (almost) skew 2nomial algebras and look for a onesided or twosided Gröbner basis theory for such algebras at a modest level. That is, we establish the existence of a skew multiplicative K basis for every skew 2nomial algebra, and we explore the existence of a (left, right, or twosided) monomial ordering for an (almost) skew 2nomial algebra. As distinct from commonly recognized algebras holding a Gröbner basis theory (such as algebras of the solvable type (KandriRody and Weispfenning, 1990) and some of their homomorphic images), a subclass of skew 2nomial algebras that have a left Gröbner basis theory but may not necessarily have a twosided Gröbner basis theory, respectively a subclass of skew 2nomial algebras that have a right Gröbner basis theory but may not necessarily have a twosided Gröbner basis theory, are determined such that numerous quantum binomial algebras (which provide binomial solutions to the Yang–Baxter equation) and their Koszul dual (GatevaIvanova and Van den Bergh, 1998; Laffaille, 2000; GatevaIvanova, 2009) are involved.  Keywords  Monomial ordering, Gröbner basis, Skew 2nomial algebra  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717110000726 
Language  English  Journal  Journal of Symbolic Computation  Volume  45  Number  9  Pages  918  942  Year  2010  Edition  0  Translation 
No  Refereed 
No 
