An extension of Buchberger's algorithm and calculationsin enveloping fields of lie algebras
Journal of Symbolic Computation
Non-commutative Gröbner bases in algebras of solvable type
Journal of Symbolic Computation
An introduction to commutative and noncommutative Gro¨bner bases
Selected papers of the second international colloquium on Words, languages and combinatorics
Gro¨bner bases in Clifford and Grassmann algebras
Journal of Symbolic Computation
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Multiplicative bases, Gröbner bases, and right Gröbner bases
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Computational ideal theory in finitely generated extension rings
Theoretical Computer Science
Letterplace ideals and non-commutative Gröbner bases
Journal of Symbolic Computation
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In this paper, we introduce (almost) skew 2-nomial algebras and look for a one-sided or two-sided Grobner 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 Grobner basis theory (such as algebras of the solvable type (Kandri-Rody and Weispfenning, 1990) and some of their homomorphic images), a subclass of skew 2-nomial algebras that have a left Grobner basis theory but may not necessarily have a two-sided Grobner basis theory, respectively a subclass of skew 2-nomial algebras that have a right Grobner basis theory but may not necessarily have a two-sided Grobner basis theory, are determined such that numerous quantum binomial algebras (which provide binomial solutions to the Yang-Baxter equation) and their Koszul dual (Gateva-Ivanova and Van den Bergh, 1998; Laffaille, 2000; Gateva-Ivanova, 2009) are involved.