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Characterizations of ordered Γ-Abel-Grassmann's groupoids

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Khan M., Amjid V., Zaman G., Yaqoob N.
Discussiones Mathematicae - General Algebra and Applications
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2014
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tom 34
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nr 1
55-73
EN
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 regular, left quasi regular, completely regular and (2,2)-regular ordered Γ-AG**-groupoids coincide. Further we have proved that every intra-regular ordered Γ-AG**-groupoid is regular but the converse is not true in general. Furthermore we have shown that non-associative regular, weakly regular, intra-regular, right regular, left regular, left quasi regular, completely regular, (2,2)-regular and strongly regular Γ-AG*-groupoids do not exist.
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Length Neutrosophic Subalgebras of BCK=BCI-Algebras

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Jun Y. B., Khan M., Smarandache F., Song S.-Z.
Bulletin of the Section of Logic
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2020
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tom 49
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nr 4
377-400
EN
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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