SUBSEMIGROUPS OF THE BICYCLIC MONOID-Reference-Cited by-同舟云学术

SUBSEMIGROUPS OF THE BICYCLIC MONOID

Published:2005-02 Issue:01 Volume:15 Page:37-57
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

DESCALÇO L.¹,RUŠKUC N.²

Affiliation:

1. Departamento de Matemática, Universidade de Aveiro, 3830-220 Aveiro, Portugal

2. Mathematical Institute, University of St. Andrews, St. Andrews KY16 9SS, Scotland, United Kingdom

Abstract

In this paper we give a description of all subsemigroups of the bicyclic monoid B. We show that there are essentially five different types of subsemigroups. One of them is the degenerate case, and the remaining four split in two groups of two, linked by the obvious anti-isomorphism of B. Each subsemigroup is characterized by a certain collection of parameters. Using our description, we determine the regular, simple and bisimple subsemigroups of B. Finally we describe algorithms for obtaining the parameters from the generating set.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196705002098

Reference15 articles.

1. A generalization of the bicyclic semigroup

2. The fundamental four-spiral semigroup

3. On the fundamental double four-spiral semigroup

4. The α-bicyclic semigroup as a topological semigroup

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