Subsemigroup Structure of the Rhotrix Bicyclic Semigroup
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Date
2026-04-14
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Published by Library and Publication Committee, University of Ilorin, Nigeria.
Abstract
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;
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Keywords
semigroup, semilattice. INTRODUCTION According to Howie[4], a semigroup is non-empty
Citation
Ahmed, B. M., Bakare, G. N. & Suleiman, Y. M. (2026). Subsemigroup Structure of the Rhotrix Bicyclic Semigroup. Centrepoint Journal (Science Edition), 30(1), 116 - 126.