Revisiting Characterization of Semigroups: Exploring limitations of Independence

Authors

  • E. H. Enyiduru Department of Mathematics, Michael Okpara University of Agriculture Umudike
  • F.A. Efiong Department of Mathematics, University of Uyo, Uyo, Akwa Ibom State, Nigeria
  • L. E. Effiong Department of Mathematics, Abia State Polytechnic, Aba, Abia State, Nigeria
  • E. O., Akak Department of Mathematics, Akwa Ibom State University, Ikot Akpaden, Nigeria
  • A. E Mfon Department of Mathematics, Akwa Ibom State University, Ikot Akpaden, Nigeria
  • M. I. Sampson Department of Mathematics, Akwa Ibom State University, Ikot Akpaden, Nigeria

Keywords:

Semigroups, Rank characterization, Independence, Counterexamples, Commutative semigroups, Non-commutative semigroups

Abstract

This paper reviews the evaluation of the characterization of semigroups Independence, generating systems  by Sampson, M. I. (see [2]), which began with studying the work of Howie and Ribeiro (see [1]) to investigate the effect of the concept of independence on semigroup generating systems. While independence is often considered fundamental in determining minimal generators for semigroups, we show instances where this notion proves inadequate. Specifically, with illustrated variations in the role of independence in Semigroup as compared to vector spaces. The study shows reliable characterization of independent generating sets that helps in the selection algorithm for the basis elements of any given semigroups.

Additional Files

Published

2025-02-20

How to Cite

Enyiduru, . E. H., Efiong, F., Effiong, L. E., Akak , E. O. ., Mfon, A. E., & Sampson, M. I. (2025). Revisiting Characterization of Semigroups: Exploring limitations of Independence. Journal of Science Education and Humanities, 8(2). Retrieved from https://akscoejoseh.org/index.php/joseh/article/view/49

Issue

Vol. 8 No. 2 (2024): Volume 8, No. 2, 2024

Section

Articles