Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of a quotient ring of $\mathbb{Z}_2\mathcal{F}$ in which a
  binomial $1 + w$ is invertible using small cancellation methods   We apply small cancellation methods originating from group theory to
investigate the structure of a quotient ring $\mathbb{Z}_2\mathcal{F} /
\mathcal{I}$, where $\mathbb{Z}_2\mathcal{F}$ is the group algebra of the free
group $\mathcal{F}$ over the field $\mathbb{Z}_2$, and the ideal $\mathcal{I}$
is generated by a single trinomial $1 + v + vw$, where $v$ is a complicated
word depending on $w$. In $\mathbb{Z}_2\mathcal{F} / \mathcal{I}$ we have $(1 +
w)^{-1} = v$, so $1 + w$ becomes invertible. We construct an explicit linear
basis of $\mathbb{Z}_2\mathcal{F} / \mathcal{I}$ (thus showing that
$\mathbb{Z}_2\mathcal{F} / \mathcal{I}\neq 0$). This is the first step in
constructing rings with exotic properties.

28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga