Subsemigroup Structure of the Rhotrix Bicyclic Semigroup
| dc.contributor.author | Ahmed, Bayo Musa | |
| dc.contributor.author | Bakare, Gatta N. | |
| dc.contributor.author | Suleiman, Y. M. | |
| dc.date.accessioned | 2026-04-27T12:10:25Z | |
| dc.date.available | 2026-04-27T12:10:25Z | |
| dc.date.issued | 2026-04-14 | |
| dc.description.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; | |
| dc.description.sponsorship | Self | |
| dc.identifier.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. | |
| dc.identifier.uri | https://uilspace.unilorin.edu.ng/handle/123456789/17644 | |
| dc.language.iso | en | |
| dc.publisher | Published by Library and Publication Committee, University of Ilorin, Nigeria. | |
| dc.relation.ispartofseries | 30; 1 | |
| dc.subject | semigroup | |
| dc.subject | semilattice. INTRODUCTION According to Howie[4] | |
| dc.subject | a semigroup is non-empty | |
| dc.title | Subsemigroup Structure of the Rhotrix Bicyclic Semigroup | |
| dc.type | Article |