2008/08/11 by Huishi Li, Li, Huishi · 1 citation
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Polynomial and algebraic computation #math.RA #msc:16W70 #msc:68W30
paper · pdf · doi:10.48550/arxiv.0808.1477
Revised version, 35 pages
arxiv created 2010/01/15 · arxiv updated 2010/02/08
In this paper, we introduce (almost) skew 2-nomial algebras and look for a one-sided or two-sided 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 2-nomial algebra, and we explore the existence of a (left, right, or two-sided) monomial ordering for an (almost) skew 2-nomial algebra. As distinct from commonly recognized algebras holding a Gröbner basis theory (such as algebras of the solvable type [K-RW] and some of their homomorphic images), a subclass of skew 2-nomial algebras that have a left Gröbner basis theory but may not necessarily have a two-sided Gröbner basis theory, respectively a subclass of skew 2-nomial algebras that have a right Gröbner basis theory but may not necessarily have a two-sided Gröbner basis theory, are determined such that numerous quantum binomial algebras (which provide binomial solutions to the Yang-baxter equation [Laf], [G-I2]) are involved.