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Embedding ample semigroups as (2,1,1)-subalgebras of inverse semigroups

Nasir Sohail, Aftab Hussain Shah, Kristo Väljako

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.

Embedding ample semigroups as (2,1,1)-subalgebras of inverse semigroups

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.

Paper Structure

This paper contains 3 sections, 17 theorems, 75 equations, 1 figure.

Table of Contents

  1. Motivation and preliminaries
  2. Answering the embedding problem for some finite ample semigroups
  3. Examples concerning left (right) ample semigroups

Key Result

Theorem 1.1

Let $T$ be an inverse semigroup. Then, for all $x\in T$ the map givne by is a partial bijection of $T$. Furthermore, the map is a monomorphism.

Figures (1)

  • Figure 1:

Theorems & Definitions (34)

  • Theorem 1.1
  • proof
  • Theorem 1.2
  • proof
  • Theorem 1.4: Gould and Kambites, Theorem 3.4
  • Corollary 1.5: Gould and Kambites, Corollary 4.3
  • Remark 1.6
  • Lemma 2.1
  • proof
  • Proposition 2.2
  • ...and 24 more