Embedding ample semigroups as (2,1,1)-subalgebras of inverse semigroups
Nasir Sohail, Aftab Hussain Shah, Kristo V\"aljako
TL;DR
This paper explores the embedding problem of ample semigroups into inverse semigroups, focusing on specific classes and providing examples of semigroups with asymmetric properties, addressing decidability issues.
Contribution
It investigates the embedding problem for certain classes of ample semigroups and provides examples illustrating asymmetries in their properties.
Findings
Embedding problem is undecidable in general.
Certain classes of ample semigroups can be embedded.
Examples of semigroups with asymmetric properties.
Abstract
The problem of embedding an ample semigroup in an inverse semigroup as a (2, 1, 1)-type subalgebra is known to be undecidable. In this article, we investigate the problem for certain classes of ample semigroups. We also give examples of semigroups that are left (respectively, right) but not right (respectively, left) ample.
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