Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalizations of Samuel's criteria for a ring to be a unique
  factorization domain   We give several criteria for a ring to be a UFD including generalizations of
some criteria due to P. Samuel. These criteria are applied to construct, for
any field k, (1) a Z-graded non-noetherian rational UFD of dimension three over
k, and (2) k-affine rational UFDs defined by trinomial relations.

29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom