L

JRRS LASU

Tropical Roots and Their Multiplicities on the Subsemigroup of Order-Decreasing and Order-Preserving Full Transformation

Authors: Risqot Garba Ibrahim1, Naimat Gatta Bakare 2, Idayat Foluke Usamot3, Ishaq Sulyman Olawoyin4, Sulaiman Awwal Akinwunmi5, Dauda Adeniran Adeshola6

Affiliations: 1. Department of Mathematics and Statistics, Kwara state University Malete, Kwara State, Nigeria
2. Department of Mathematics, Faculty of Physical Science, University of Ilorin, Ilorin
3. Department of Mathematics, Faculty of Physical Science, University of Ilorin, Ilorin
4. Department of Mathematics and Statistics, Kwara state University Malete, Kwara State, Nigeria
5. Department of Mathematics, Federal University of Kashere, Gombe State, Nigeria.
6. Department of Mathematics and Statistics, , Kwara state University Malete, Kwara State, Nigeria Correspondence Naimat Gatta Bakare Depart

Abstract

Let Ω_υ={1,2,3,--,υ} be ordered finite set. The tropical geometry was utilized to analyze the subsemigroup of order-decreasing and order-preserving full transformation semigroups, denoted as D_υ∩O_υ= C_υ . The elements of classical algebra within C_υ were transformed into tropical polynomials, allowing for the determination of tropical roots and their multiplicities through the tropical curve, which was visualized using {GeoGebra}.

Keywords

Semigroup Full Transformation Subsemigroup of Order-Decreasing and Order-Preserving Tropical Polynomial Tropical Curve and Multiplicity and height