Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Zariski-like topology on the ideal spectrum of a ring   The purpose of this paper is to introduce a Zariski-like topology on the
spectrum of all proper ideals of a ring. We show that the space is T_0,
quasi-compact, and every irreducible closed subset has a unique generic point.
Furthermore, this space is weaker than a spectral space and if the ring has a
non-trivial idempotent element then the space has a closed disconnected
subspace.

5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph