Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization of adequate semigroups by forbidden subsemigroups   A semigroup is \emph{amiable} if there is exactly one idempotent in each
$\mathcal{R}^*$-class and in each $\mathcal{L}^*$-class. A semigroup is
\emph{adequate} if it is amiable and if its idempotents commute. We
characterize adequate semigroups by showing that they are precisely those
amiable semigroups which do not contain isomorphic copies of two particular
nonadequate semigroups as subsemigroups.

13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th