Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Right $P$-comparable semigroups   In this paper we introduce the notion of right waist and right comparizer
ideals for semigroups. In particular, we study the ideal theory of semigroups
containing right waists and right comparizer ideals. We also study those
properties of right cones that can be carried over to right $P$-comparable
semigroups. We give sufficient and necessary conditions on the set of nilpotent
elements of a semigroup to be an ideal. We provide several equivalent
characterizations for a right ideal being a right waist. In one of our main
result we show that in a right $P_1$-comparable semigroup with left
cancellation law, a prime segment $P_2\subset P_1$ is Archimedean, simple or
exceptional, extending a similar result of right cones to $P$-comparable
semigroups.

22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an