Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the intersection graphs of modules and rings   We classify modules and rings with some specific properties of their
intersection graphs. In particular, we describe rings with infinite
intersection graphs containing maximal left ideals of finite degree. This
answers a question raised in [A2]. We also generalize this result to modules,
i.e. we get the structure theorem of modules for which their intersection
graphs are infinite and contain maximal submodules of finite degree.
Furthermore we omit the assumption of maximality of submodules and still get a
satisfactory characterization of such modules. In addition we show that, if the
intersection graph of a module is infinite but its clique number is finite,
then the clique and chromatic numbers of the graph coincide. This fact was
known earlier only in some particular cases. It appears that such equality
holds also in the complement graph.

33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
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The categories of this paper are: q-alg
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg