Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposition of intra-regular $po$-$\Gamma$-semigroups into simple
  components   We keep the definition of intra-regularity (left regularity) of
$po$-$\Gamma$-semigroups introduced in arXiv: 1511.00679 which is absolutely
necessary for the investigation. Being able to describe the form of the
elements of the principal filter by using this definition, we study the
decomposition of an intra-regular $po$-$\Gamma$-semigroup into simple
components. Then we prove that a $po$-$\Gamma$-semigroup $M$ is intra-regular
and the ideals of $M$ form a chain if and only if $M$ is a chain of simple
semigroups. Moreover, a $po$-$\Gamma$-semigroup $M$ is intra-regular and the
ideals of $M$ form a chain if and only if the ideals of $M$ are prime. Finally,
for an intra-regular $po$-$\Gamma$-semigroup $M$, the set $\{(x)_{\cal N} \mid
x\in M\}$ coincides with the set of all maximal simple subsemigroups of $M$. A
decomposition of left regular and left duo $po$-$\Gamma$-semigroup into left
simple components has been also given.

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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: econ
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio