On the semigroup of finite order-preserving partial injective contraction mappings

F. Al-Kharousi; G. U. Garba; M. J. Ibrahim; A. T. Imam; A. Umar

doi:10.1007/s13370-025-01259-z

On the semigroup of finite order-preserving partial injective contraction mappings

F. Al-Kharousi
, G. U. Garba
, M. J. Ibrahim
, A. T. Imam
, A. Umar

Mathematics

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

Abstract

We initiate the algebraic study of the semigroup of one-to-one order-preserving partial contraction mappings of a totally ordered set {1,2,…,n}, which we denote by OCIn. In particular, we characterise the Green’s relations and their starred analogues in OCIn. We also compute the rank of OCIn as 2n-1.

Original language	British English
Article number	48
Journal	Afrika Matematika
Volume	36
Issue number	1
DOIs	https://doi.org/10.1007/s13370-025-01259-z
State	Published - Mar 2025

Keywords

Contraction map
Green’s relations
Inverse ideal
Isometry
Order-preserving map
Shifting index
Starred Green’s relations

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10.1007/s13370-025-01259-z

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abstract = "We initiate the algebraic study of the semigroup of one-to-one order-preserving partial contraction mappings of a totally ordered set \{1,2,…,n\}, which we denote by OCIn. In particular, we characterise the Green{\textquoteright}s relations and their starred analogues in OCIn. We also compute the rank of OCIn as 2n-1.",

keywords = "Contraction map, Green{\textquoteright}s relations, Inverse ideal, Isometry, Order-preserving map, Shifting index, Starred Green{\textquoteright}s relations",

author = "F. Al-Kharousi and Garba, \{G. U.\} and Ibrahim, \{M. J.\} and Imam, \{A. T.\} and A. Umar",

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AU - Garba, G. U.

AU - Ibrahim, M. J.

AU - Imam, A. T.

AU - Umar, A.

N1 - Publisher Copyright: © African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2025.

PY - 2025/3

Y1 - 2025/3

N2 - We initiate the algebraic study of the semigroup of one-to-one order-preserving partial contraction mappings of a totally ordered set {1,2,…,n}, which we denote by OCIn. In particular, we characterise the Green’s relations and their starred analogues in OCIn. We also compute the rank of OCIn as 2n-1.

AB - We initiate the algebraic study of the semigroup of one-to-one order-preserving partial contraction mappings of a totally ordered set {1,2,…,n}, which we denote by OCIn. In particular, we characterise the Green’s relations and their starred analogues in OCIn. We also compute the rank of OCIn as 2n-1.

KW - Contraction map

KW - Green’s relations

KW - Inverse ideal

KW - Isometry

KW - Order-preserving map

KW - Shifting index

KW - Starred Green’s relations

UR - https://www.scopus.com/pages/publications/85218239995

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DO - 10.1007/s13370-025-01259-z

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VL - 36

JO - Afrika Matematika

JF - Afrika Matematika

IS - 1

M1 - 48

ER -

On the semigroup of finite order-preserving partial injective contraction mappings

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Keywords

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