Search results for: idempotent semi-modules

3 Digraph Generated by Idempotents in Certain Finite Semigroup of Mappings

Authors: Hassan Ibrahim, Moses Anayo Mbah

Abstract:

The idempotent generators in a finite full transformation and the digraph of full transformation semi group have been an interesting area of research in group theory. In this work, it characterized some idempotent elements in full transformation semigroup T_n by counting the strongly connected and disconnected digraphs, and also the weakly and unilaterally connected digraphs. The order for those digraphs was further obtained in T_n.

Keywords: digraphs, indempotent, semigroup, transformation

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2 Classification of Tropical Semi-Modules

Authors: Wagneur Edouard

Abstract:

Tropical algebra is the algebra constructed over an idempotent semifield S. We show here that every m-dimensional tropical module M over S with strongly independent basis can be embedded into Sm, and provide an algebraic invariant -the Γ-matrix of M- which characterises the isomorphy class of M. The strong independence condition also yields a significant improvement to the Whitney embedding for tropical torsion modules published earlier We also show that the strong independence of the basis of M is equivalent to the unique representation of elements of M. Numerous examples illustrate our results.

Keywords: classification, idempotent semi-modules, strong independence, tropical algebra

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1 Congruences Induced by Certain Relations on Ag**-Groupoids

Authors: Faisal Yousafzai, Murad-ul-Islam Khan, Kar Ping Shum

Abstract:

We introduce the concept of partially inverse AG**-groupoids which is almost parallel to the concepts of E-inversive semigroups and E-inversive E-semigroups. Some characterization problems are provided on partially inverse AG**-groupoids. We give necessary and sufficient conditions for a partially inverse AG**-subgroupoid E to be a rectangular band. Furthermore, we determine the unitary congruence η on a partially inverse AG**-groupoid and show that each partially inverse AG**-groupoid possesses an idempotent separating congruence μ. We also study anti-separative commutative image of a locally associative AG**-groupoid. Finally, we give the concept of completely N-inverse AG**-groupoid and characterize a maximum idempotent separating congruence.

Keywords: AG**-groupoids, congruences, inverses, rectangular band

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