Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Special Semigroups Derived From an Arbitrary Semigroup   Let $S$ be a semigroup, $\Lambda$ a non-empty set and $P$ a mapping of
$\Lambda$ into $S$. The set $S\times \Lambda$ together with the operation
$\circ _P$ defined by $(s, \lambda)\circ _P(t, \mu )=(sP(\lambda)t, \mu )$ form
a semigroup which is denoted by $(S, \Lambda , \circ _P)$. Using this
construction, we prove a common connection between the semigroups $S$,
$S/\theta$ and $S/\theta ^*=(S/\theta)/(\theta ^*/\theta)$, where $\theta$ and
$\theta ^*/\theta$ are the kernels of the right regular representations of $S$
and $S/\theta$, respectively. We also prove an embedding theorem for the
semigroup $(S, S/\theta , \circ _p)$, where $S$ is a left equalizer simple
semigroup without idempotents, and $P$ maps every $\theta$-class of $S$ into
itself.

31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an