On the question of embedding a semigroup into an idempotent generated one
Group Theory
2019-06-04 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1205.3454,
title = {On the question of embedding a semigroup into an idempotent generated one},
author = {Luis Oliveira},
journal= {arXiv preprint arXiv:1205.3454},
year = {2019}
}
Comments
22 pages