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.
Digital Object Identifier (DOI)
S. Al-Kadi, Deena and A. Hosny, Rodyna
"G+-algebra, Filters and Upper sets,"
Applied Mathematics & Information Sciences: Vol. 10
, Article 16.
Available at: https://dc.naturalspublishing.com/amis/vol10/iss6/16