Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regular local rings of dimension four and Gorenstein syzygetic prime
  ideals   Let $R$ be a Noetherian local ring. We prove that $R$ is regular of dimension
at most four if, and only if, every prime ideal, defining a Gorenstein quotient
ring, is syzygetic. We deduce a characterization of these rings in terms of the
Andr\'e-Quillen homology.

25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph