Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Commutative rings with finite quotient fields   We consider the class of all commutative reduced rings for which there exists
a finite subset T of A such that all projections on quotients by prime ideals
of A are surjective when restricted to T. A complete structure theorem is given
for this class of rings, and it is studied its relation with other finiteness
conditions on the quotients of a ring over its prime ideals.

22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom