Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On inverse ordered semigroups   The purpose of this paper is to study the generalization of inverse
semigroups (without order). An ordered semigroup S is called an inverse ordered
semigroup if for every a 2 S, any two inverses of a are H-related. We prove
that an ordered semigroup is complete semilattice of t-simple ordered
semigroups if and only if it is completely regular and inverse. Furthermore
characterizations of inverse ordered semigroups have been characterized by
their ordered idempotents.

26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph