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Journal of Semigroup Theory and Applications ISSN 2051-2937

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J. Semigroup Theory Appl. 2026 (2026), Article ID 2

Quasi-idempotents in finite semigroup of full order-preserving transformations

A. T. Imam, I. A. Bayero, A. Idris

PDF (132.5 KB) https://doi.org/10.28919/jsta/9723

Abstract

Let Xn be the finite set {1,2,...,n} and On,r = {α∈On: |imα| ≤ r} (where 1 ≤ r ≤ n-1) be the ideals of a semigroup of full order-preserving transformations on the finite set. In this article, a study of quasi-idempotent elements via idempotents and generating set in the ideals of finite semigroup of full order-preserving transformations is carried out. The quasi-idempotent elements are characterised in this semigroup and that it is quasi-idempotent generated via idempotents. Moreover, the minimum length of a factorisations into products of quasi-idempotent elements is obtained.

Published
20 February 2026
Volume
2026 (2026)
License
CC BY 3.0

Copyright © 2026 A. T. Imam, I. A. Bayero, A. Idris. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

A. T. Imam, I. A. Bayero, A. Idris, Quasi-idempotents in finite semigroup of full order-preserving transformations, J. Semigroup Theory Appl. 2026 (2026), 2. https://doi.org/10.28919/jsta/9723

BibTeX
@article{Imam2026,
  author  = {Imam, A. T. and Bayero, I. A. and Idris, A.},
  title   = {Quasi-idempotents in finite semigroup of full order-preserving transformations},
  journal = {J. Semigroup Theory Appl.},
  volume  = {2026},
  year    = {2026},
  pages   = {2},
  doi     = {10.28919/jsta/9723}
}