A classification of disjoint unions of two or three copies of the free monogenic semigroup

N. Abu-Ghazalh; J.D. Mitchell; Y. Péresse; Nik Ruskuc

doi:10.1007/s00233-014-9638-4

A classification of disjoint unions of two or three copies of the free monogenic semigroup

N. Abu-Ghazalh, J.D. Mitchell, Y. Péresse, Nik Ruskuc

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that, up to isomorphism and anti-isomorphism, there are only two types of semigroups which are the union of two copies of the free monogenic semigroup. Similarly, there are only nine types of semigroups which are the union of three copies of the free monogenic semigroup. We provide finite presentations for semigroups of each of these types.

Original language	English
Pages (from-to)	53-61
Number of pages	9
Journal	Semigroup Forum
Volume	91
Issue number	1
Early online date	19 Dec 2014
DOIs	https://doi.org/10.1007/s00233-014-9638-4
Publication status	Published - Aug 2015

Keywords

Semigroups
Decompositions
Free semigroup
Finite presentations

Access to Document

10.1007/s00233-014-9638-4

Theory of Semigroups: Representation theory of Semigroups
Ruskuc, N. (PI)
EPSRC
1/04/12 → 30/09/15
Project: Standard
Automata Languages Decidability: Automata, Languages, Decidability in Algebra
Ruskuc, N. (PI) & Quick, M. (CoI)
EPSRC
1/03/10 → 31/05/14
Project: Standard

Cite this

@article{21c2c40a2063497a81c2a9bfab548bf5,

title = "A classification of disjoint unions of two or three copies of the free monogenic semigroup",

abstract = "We prove that, up to isomorphism and anti-isomorphism, there are only two types of semigroups which are the union of two copies of the free monogenic semigroup. Similarly, there are only nine types of semigroups which are the union of three copies of the free monogenic semigroup. We provide finite presentations for semigroups of each of these types.",

keywords = "Semigroups, Decompositions, Free semigroup, Finite presentations",

author = "N. Abu-Ghazalh and J.D. Mitchell and Y. P{\'e}resse and Nik Ruskuc",

year = "2015",

month = aug,

doi = "10.1007/s00233-014-9638-4",

language = "English",

volume = "91",

pages = "53--61",

journal = "Semigroup Forum",

issn = "0037-1912",

publisher = "Springer",

number = "1",

}

TY - JOUR

T1 - A classification of disjoint unions of two or three copies of the free monogenic semigroup

AU - Abu-Ghazalh, N.

AU - Mitchell, J.D.

AU - Péresse, Y.

AU - Ruskuc, Nik

PY - 2015/8

Y1 - 2015/8

N2 - We prove that, up to isomorphism and anti-isomorphism, there are only two types of semigroups which are the union of two copies of the free monogenic semigroup. Similarly, there are only nine types of semigroups which are the union of three copies of the free monogenic semigroup. We provide finite presentations for semigroups of each of these types.

AB - We prove that, up to isomorphism and anti-isomorphism, there are only two types of semigroups which are the union of two copies of the free monogenic semigroup. Similarly, there are only nine types of semigroups which are the union of three copies of the free monogenic semigroup. We provide finite presentations for semigroups of each of these types.

KW - Semigroups

KW - Decompositions

KW - Free semigroup

KW - Finite presentations

U2 - 10.1007/s00233-014-9638-4

DO - 10.1007/s00233-014-9638-4

M3 - Article

AN - SCOPUS:84937970318

SN - 0037-1912

VL - 91

SP - 53

EP - 61

JO - Semigroup Forum

JF - Semigroup Forum

IS - 1

ER -

A classification of disjoint unions of two or three copies of the free monogenic semigroup

Abstract

Keywords

Access to Document

Fingerprint

Projects

Theory of Semigroups: Representation theory of Semigroups

Automata Languages Decidability: Automata, Languages, Decidability in Algebra

Cite this