On the semigroups of partial one-to-one order-decreasing finite transformations

Abdullahi Umar

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Let In be the symmetric inverse semigroup on Xn = {1,…,n}, let SIn be the subsemigroup of strictly partial one-to-one self-maps of Xn and let [formula-omitted] be the semigroup of all partial one-to-one decreasing maps including the empty or zero map of Xn. In this paper it is shown that In is an (irregular, for n ≥ 2) type A semigroup with n D-classes and d=g Further, it is shown that In- is generated by the n(n + 1)/2 quasi-idempotents in Jn-1.

Original languageEnglish
Pages (from-to)355-363
Number of pages9
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume123
Issue number2
DOIs
Publication statusPublished - 1993

Fingerprint

Semigroup
Partial
Inverse Semigroup
Idempotent
Irregular
Strictly
Zero
Class

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the semigroups of partial one-to-one order-decreasing finite transformations. / Umar, Abdullahi.

In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 123, No. 2, 1993, p. 355-363.

Research output: Contribution to journalArticle

@article{92082f1d48324564b8d95b73c4339805,
title = "On the semigroups of partial one-to-one order-decreasing finite transformations",
abstract = "Let In be the symmetric inverse semigroup on Xn = {1,…,n}, let SIn be the subsemigroup of strictly partial one-to-one self-maps of Xn and let [formula-omitted] be the semigroup of all partial one-to-one decreasing maps including the empty or zero map of Xn. In this paper it is shown that In is an (irregular, for n ≥ 2) type A semigroup with n D-classes and d=g Further, it is shown that In- is generated by the n(n + 1)/2 quasi-idempotents in Jn-1.",
author = "Abdullahi Umar",
year = "1993",
doi = "10.1017/S0308210500025737",
language = "English",
volume = "123",
pages = "355--363",
journal = "Proceedings of the Royal Society of Edinburgh Section A: Mathematics",
issn = "0308-2105",
publisher = "Cambridge University Press",
number = "2",

}

TY - JOUR

T1 - On the semigroups of partial one-to-one order-decreasing finite transformations

AU - Umar, Abdullahi

PY - 1993

Y1 - 1993

N2 - Let In be the symmetric inverse semigroup on Xn = {1,…,n}, let SIn be the subsemigroup of strictly partial one-to-one self-maps of Xn and let [formula-omitted] be the semigroup of all partial one-to-one decreasing maps including the empty or zero map of Xn. In this paper it is shown that In is an (irregular, for n ≥ 2) type A semigroup with n D-classes and d=g Further, it is shown that In- is generated by the n(n + 1)/2 quasi-idempotents in Jn-1.

AB - Let In be the symmetric inverse semigroup on Xn = {1,…,n}, let SIn be the subsemigroup of strictly partial one-to-one self-maps of Xn and let [formula-omitted] be the semigroup of all partial one-to-one decreasing maps including the empty or zero map of Xn. In this paper it is shown that In is an (irregular, for n ≥ 2) type A semigroup with n D-classes and d=g Further, it is shown that In- is generated by the n(n + 1)/2 quasi-idempotents in Jn-1.

UR - http://www.scopus.com/inward/record.url?scp=84972102836&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972102836&partnerID=8YFLogxK

U2 - 10.1017/S0308210500025737

DO - 10.1017/S0308210500025737

M3 - Article

AN - SCOPUS:84972102836

VL - 123

SP - 355

EP - 363

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 2

ER -