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

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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

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