On the Ranks of Semigroups of Transformations on a Finite Set with Restricted Range-Reference-Cited by-同舟云学术

On the Ranks of Semigroups of Transformations on a Finite Set with Restricted Range

Published:2014-06-24 Issue:03 Volume:21 Page:497-510
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Fernandes Vítor H.¹²,Sanwong Jintana³⁴

Affiliation:

1. Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Monte da Caparica, 2829-516 Caparica, Portugal

2. Centro de Álgebra da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

3. Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

4. Material Science Research Center, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Abstract

Let [Formula: see text] be the semigroup of all partial transformations on X, [Formula: see text] and [Formula: see text] be the subsemigroups of [Formula: see text] of all full transformations on X and of all injective partial transformations on X, respectively. Given a non-empty subset Y of X, let [Formula: see text], [Formula: see text] and [Formula: see text]. In 2008, Sanwong and Sommanee described the largest regular subsemigroup and determined Green's relations of [Formula: see text]. In this paper, we present analogous results for both [Formula: see text] and [Formula: see text]. For a finite set X with |X| ≥ 3, the ranks of [Formula: see text], [Formula: see text] and [Formula: see text] are well known to be 4, 3 and 3, respectively. In this paper, we also compute the ranks of [Formula: see text], [Formula: see text] and [Formula: see text] for any proper non-empty subset Y of X.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1005386714000431

Reference10 articles.

1. Idempotents in partial transformation semigroups

2. On the ranks of certain finite semigroups of transformations

3. Idempotent rank in finite full transformation semigroups

4. THE IDEAL STRUCTURE OF SEMIGROUPS OF TRANSFORMATIONS WITH RESTRICTED RANGE

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