Browsing by Author "Suleiman, Y. M."
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Item Subsemigroup Structure of the Rhotrix Bicyclic Semigroup(Published by Library and Publication Committee, University of Ilorin, Nigeria., 2026-04-14) Ahmed, Bayo Musa; Bakare, Gatta N.; Suleiman, Y. M.This paper investigates the subsemigroup structure of the rhotrix bicyclic semigroup obtained as a coordinatewise extension of the classical bicyclic semigroup. Order-defined subsemigroups determined by the componenetwise relations , and = are introduced and analyzed. It is shown that the order-decreasing subsemigroup forms a subsemigroup but is neither regular nor inverse, with its regular elements coinciding precisely with the diagonal elements. The order-increasing subsemigroup is established to be anti-isomorphic to the order-decreasing case, while the diagonal subsemigroup is proved to be commutative idempotent semigroup and is isomorphic to a semilattice under componentwise maximum. These results provide structural classification of order-defined subsemigroups of the rhotrix bicyclic semigroup. Keywords:Rhotrix bicyclic semigroup; order-defined subsemigroup; regularity; idempotent structure;