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Characterizations of ordered Γ-Abel-Grassmann's groupoids

Madad Khan;  Venus Amjid;  Gul Zaman;  Naveed Yaqoob — 2014

Discussiones Mathematicae - General Algebra and Applications

In this paper, we introduced the concept of ordered Γ-AG-groupoids, Γ-ideals and some classes in ordered Γ-AG-groupoids. We have shown that every Γ-ideal in an ordered Γ-AG**-groupoid S is Γ-prime if and only if it is Γ-idempotent and the set of Γ-ideals of S is Γ-totally ordered under inclusion. We have proved that the set of Γ-ideals of S form a semilattice, also we have investigated some classes of ordered Γ-AG**-groupoid and it has shown that weakly regular, intra-regular, right regular, left...

Length Neutrosophic Subalgebras of BCK=BCI-Algebras

Young Bae Jun;  Madad Khan;  Florentin Smarandache;  Seok-Zun Song — 2020

Bulletin of the Section of Logic

Given i, j, k ∈ {1,2,3,4}, the notion of (i, j, k)-length neutrosophic subalgebras in BCK=BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebras are provided.

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