On Signed Full Transformation Semigroup of a Finite Set

Authors

  • Usman Mohammed Yusuf
    Department of Mathematics, Federal University of Lafia
  • Dr. Mbah Moses A.
    Department of Mathematics, Federal University of Lafia, Lafia, Nasarawa State
  • Alaku A. Abimiku
    Department of Basic Science, College of Agriculture, Science and Technology, Lafia, Nasarawa State

Keywords:

Semigroup , Signed transformation , Order preserving transformation , Order decreasing transformation , Idempotents

Abstract

If we define [n] = {1,2,3,...,n} and [n*] = {±1,±2,±3...,±n}.  A map α: [n] → [n*] is called a signed transformation on [n]. The collection of all these maps together with composition forms a semigroup called a signed transformation semigroup. Given that dom(α) = [n],  the signed transformation semigroup will be called a signed full transformation semigroup on [n]. In this paper, we obtain formulas that count the number of elements in the semigroups of order decreasing, order preserving and order decreasing signed transformations on [n]. We equally do same for the sub-semigroup of the signed transformation semigroup consisting only of idempotents.

Dimensions

Garba, G.U. (1990). Idempotents in partial transformation semigroups. Proc. Of the Royal Society of Edinburgh. 116, 359 -366.

Howie, J. M. (1995). Fundamentals of semigroup theory. New york, NY, USA: Oxford University press.

Imam, A.T. and Tal, P. P. (2019). On Maximum Works and Stretches Performed by Transformations of a Finite Set. Journal of the Nigerian Association of Mathematical Physics. 53(Nov). pp 21-28. http://dx.doi.org/10.5539/mas.v16n2p23.

James, G. D. and Kerber, A. (1981). The representation theory of the symmetric group. Encycl. Math.Appl,16.https://archive.org/search.php?query=external identifier%3A%22urn%3Aoclc%3Arecord%3A1151161717%22

James, G. D. and Kerber, A. (1981). The Representation Theory of the Symmetric Group. Addison-Wesley, Reading, M.A.

Mogbonju, M. M., Adeniji, A. O., and Ogunleke, I. A. (2019). Signed singular mappings transformation semigroup. International Journal of Mathematics and Statistics Studies, 7:45–54. https://doi.org/10.37745/ijmss.13.

Mogbonju, M. M. and Azeez, R. A. (2018). On some signed semigroups of order-preserving transformation. International Journal of Mathematics and Statistics Studies, 6:38–45. https://doi.org/10.37745/ijmss.13.

Tal, P. P., Mahmud, M. S., Mbah, M. A. & Ndubuisi, R. U. (2022). Maximum and Minimum Works Performed by signed transformation semigroup. Modern Applied Science,16(2). Canadian Centre of Science and Education.

On Signed Transformation

Published

10-04-2025

How to Cite

On Signed Full Transformation Semigroup of a Finite Set. (2025). FULafia Journal of Science and Technology , 9(1), 54-56. https://doi.org/10.62050/fjst2025.v9n1.510

Issue

Vol. 9 No. 1 (2025): Vol. 9 No. 1 (March, 2025): Fulafia Journal of Science and Technology (FJST)

Section

Physical Sciences
Copyright & Licensing

How to Cite

On Signed Full Transformation Semigroup of a Finite Set. (2025). FULafia Journal of Science and Technology , 9(1), 54-56. https://doi.org/10.62050/fjst2025.v9n1.510

Most read articles by the same author(s)

Similar Articles

11-20 of 51

You may also start an advanced similarity search for this article.