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Saudi Arabia


In this paper, a new notion named G+-algebra is introduced as a dual G-algebra. Then the relation between G+-algebra with number of abstract algebras including dual BCK-algebra, implication algebra, BE-algebra and J-algebra is investigated and some properties of G+-algebra are studied. Moreover, a binary relation on G+-algebra is defined and proved that it forms a partially ordered relation. Finally, considering G+-algebra, filters and upper sets are studied and related properties are discussed providing an equivalent condition of a filter and finding the relation between filters and upper sets.

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