Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Commutative rings with every non-maximal ideal finitely generated   In commutative ring theory, there is a theorem of Cohen which states that if
in a commutative ring all prime ideals are finitely generated then every ideal
is finitely generated. However, it is known that having only maximal ideals
finitely generated doesn't imply all ideals be finitely generated. In his
article we ask the question that what happens if we assume all non-maximal
ideals are finitely generated, and we answer the question by showing that
indeed then all maximal ideals are also finitely generated i.e. the ring
becomes Noetherian.

17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int