Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the question of embedding a semigroup into an idempotent generated
  one   In this paper we present a new embedding of a semigroup into a semiband
(idempotent-generated semigroup) of depth 4 (every element is the product of 4
idempotents) using a semidirect product construction. Our embedding does not
assume that S is a monoid (although it assumes a weaker condition), and works
also for (non-monoid) regular semigroups. In fact, this semidirect product is
particularly useful for regular semigroups since we can defined another
embedding for these semigroups into a smaller semiband of depth 2. We shall
then compare our construction with other known embeddings, and we shall see
that some properties of S are preserved by our embedding.

32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex