Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Classification of the Projective Lines over Small Rings   A compact classification of the projective lines defined over (commutative)
rings (with unity) of all orders up to thirty-one is given. There are
altogether sixty-five different types of them. For each type we introduce the
total number of points on the line, the number of points represented by
coordinates with at least one entry being a unit, the cardinality of the
neighbourhood of a generic point of the line as well as those of the
intersections between the neighbourhoods of two and three mutually distant
points, the number of `Jacobson' points per a neighbourhood, the maximum number
of pairwise distant points and, finally, a list of representative/base rings.
The classification is presented in form of a table in order to see readily not
only the fine traits of the hierarchy, but also the changes in the structure of
the lines as one goes from one type to the other. We hope this study will serve
as an impetus to a search for possible applications of these remarkable
geometries in physics, chemistry, biology and other natural sciences as well.

36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys