G+-algebra, Filters and Upper sets

Authors

Deena S. Al-Kadi, Department of Mathematics and Statistics, College of Science, Taif University, Al-Hawiya, P.O. Box 888, Taif 21974 , Saudi ArabiaFollow
Rodyna A. Hosny, Department of Mathematics and Statistics, College of Science, Taif University, Al-Hawiya, P.O. Box 888, Taif 21974 , Saudi Arabia\\ Department of Mathematics, College of Science, Zagazig University, Zagazig, EgyptFollow

Author Country (or Countries)

Saudi Arabia

Abstract

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)

http://dx.doi.org/10.18576/amis/100616

Recommended Citation

S. Al-Kadi, Deena and A. Hosny, Rodyna (2016) "G+-algebra, Filters and Upper sets," Applied Mathematics & Information Sciences: Vol. 10: Iss. 6, Article 16.
DOI: http://dx.doi.org/10.18576/amis/100616
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss6/16