Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A constructive proof of the Wedderburn-Artin theorem   In this short note, we use the idempotent decomposition to give an explicit
isomorphism from a semisimple Artinian ring to an external direct sum of finite
full matrix rings over division rings.

34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex