Subsemigroup Structure of the Rhotrix Bicyclic Semigroup

dc.contributor.authorAhmed, Bayo Musa
dc.contributor.authorBakare, Gatta N.
dc.contributor.authorSuleiman, Y. M.
dc.date.accessioned2026-04-27T12:10:25Z
dc.date.available2026-04-27T12:10:25Z
dc.date.issued2026-04-14
dc.description.abstractThis 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.sponsorshipSelf
dc.identifier.citationAhmed, 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.urihttps://uilspace.unilorin.edu.ng/handle/123456789/17644
dc.language.isoen
dc.publisherPublished by Library and Publication Committee, University of Ilorin, Nigeria.
dc.relation.ispartofseries30; 1
dc.subjectsemigroup
dc.subjectsemilattice. INTRODUCTION According to Howie[4]
dc.subjecta semigroup is non-empty
dc.titleSubsemigroup Structure of the Rhotrix Bicyclic Semigroup
dc.typeArticle

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