Products of Nilpotents in Partial Transformation Semigroups using Digraphic Paths and Chains

Authors

  • Usman Mohammed Yusuf
    Department of Mathematics, Federal University of Lafia
  • Babayo A. M.
    Department of Mathematics and Statistics, Federal University of Kashere, Nigeria
  • Mbah M. A.
    Department of Mathematics, Federal University of Lafia, Lafia, Nasarawa State

Keywords:

Depth formula , Full transformation , Idempotents , Nilpotents , Semigroups

Abstract

In this paper, we investigate the factorization of singular partial self-maps on a finite set into products of the least number of nilpotent elements. This research demonstrates that the semigroup of such maps can be expressed within a union of nilpotent-generated sets, specifically up to the third power. Some of our key findings include the determination of the nilpotent rank and the nilpotent depth for these maps, which vary based on whether the set size is even or odd. Additionally, this study surveys the relationship between these results and Stirling numbers, leveraging the Vagner Theorem and digraphic representations. We also examine stable quasi-idempotents, which correspond to specific digraphic paths and chains, providing further insights into the structure of partial
transformation semigroups. 

Dimensions

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Published

08-05-2025

How to Cite

Products of Nilpotents in Partial Transformation Semigroups using Digraphic Paths and Chains. (2025). FULafia Journal of Science and Technology , 9(1), 81-87. https://doi.org/10.62050/fjst2025.v9n1.511

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

Products of Nilpotents in Partial Transformation Semigroups using Digraphic Paths and Chains. (2025). FULafia Journal of Science and Technology , 9(1), 81-87. https://doi.org/10.62050/fjst2025.v9n1.511

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