Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $F$-rationality of two-dimensional graded rings with a rational
  singularity   It is known that a two-dimensional $F$-rational ring has a rational
singularity. However a two-dimensional ring with a rational singularity is not
$F$-rational in general. In this paper, we investigate $F$-rationality of a
two-dimensional graded ring with a rational singularity in terms of the
multiplicity. Moreover, we determine when a two-dimensional graded ring with a
rational singularity and a small multiplicity is $F$-rational.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin