Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: When an amalgamated duplication of a ring along an ideal is
  quasi-Frobenius   In this paper, we characterize an amalgamated duplication of a ring $R$ along
a proper ideal $I$, $R\bowtie I$, which is quasi-Frobenius.

11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol