NEARLY COMPLETE STRONG SEMILATTICE OF LEFT GROUPS

Aftab Hussain Shah     (Department of Mathematics, Central University of Kashmir, Ganderbal-191201, India)
Shariq Ali     (Department of Mathematics, Central University of Kashmir, Ganderbal-191201, India)
Dilawar Juneed Mir     (Department of Mathematics, University Institute of Sciences, Chandigarh University, NH-05 Chandigarh-Ludhiana Highway, Mohali, Punjab, 140413, India)

Abstract


This study provides significant insights into the structure and behavior of a strong semilattice of left groups, establishing a solid foundation for future research in this domain. The work commences by presenting significant findings about endomorphisms and inner automorphisms of these semigroups. It subsequently explores their centers and analyzes the corresponding group of units. Our findings significantly extend the theory by generalizing nearly-complete Clifford monoids, enhancing the comprehension of these intricate algebraic structures and facilitating further investigation and applications.

Keywords


Semigroups, Groups, Left groups, Strong Semilattice of left groups, Regular, Inverse, Bijective, Surjective, Injective, Image trivial

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References


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DOI: http://dx.doi.org/10.15826/umj.2026.1.009

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