Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Looking for Groebner Basis Theory for (Almost) Skew 2-Nomial Algebras   In this paper, we introduce (almost) skew 2-nomial algebras and look for a
one-sided or two-sided Gr\"obner 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 Gr\"obner 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 Gr\"obner basis
theory but may not necessarily have a two-sided Gr\"obner basis theory,
respectively a subclass of skew 2-nomial algebras that have a right Gr\"obner
basis theory but may not necessarily have a two-sided Gr\"obner basis theory,
are determined such that numerous quantum binomial algebras (which provide
binomial solutions to the Yang-baxter equation [Laf], [G-I2]) are involved.

16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th