Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Congruences on bicyclic extensions of a linearly ordered group   In the paper we study inverse semigroups $\mathscr{B}(G)$,
$\mathscr{B}^+(G)$, $\bar{\mathscr{B}}(G)$ and $\bar{\mathscr{B}}\,^+(G)$ which
are generated by partial monotone injective translations of a positive cone of
a linearly ordered group $G$. We describe Green's relations on the semigroups
$\mathscr{B}(G)$, $\mathscr{B}^+(G)$, $\bar{\mathscr{B}}(G)$ and
$\bar{\mathscr{B}}\,^+(G)$, their bands and show that they are simple, and
moreover the semigroups $\mathscr{B}(G)$ and $\mathscr{B}^+(G)$ are bisimple.
We show that for a commutative linearly ordered group $G$ all non-trivial
congruences on the semigroup $\mathscr{B}(G)$ (and $\mathscr{B}^+(G)$) are
group congruences if and only if the group $G$ is archimedean. Also we describe
the structure of group congruences on the semigroups $\mathscr{B}(G)$,
$\mathscr{B}^+(G)$, $\bar{\mathscr{B}}(G)$ and $\bar{\mathscr{B}}\,^+(G)$.

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The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: econ
25
The categories of this paper are: patt-sol