Shahrood University of TechnologyJournal of Algebraic Systems2345-512812120240901BORDERED GE-ALGEBRAS4358283410.22044/jas.2022.11184.1558ENRavikumar BandaruDepartment of Mathematics, GITAM(Deemed to be University), P.O. Box 502329,
Telangana State, India0000-0001-8661-7914Mehmet Ali OzturkDepartment of Mathematics, Faculty of Arts and Sciences, AdÄ±yaman University,
P.O. Box 02040, AdÄ±yaman, TurkeyYoung Bae JunDepartment of Mathematics Education, Gyeongsang National University, P.O. Box
52828, Jinju, Korea.0000-0002-0181-8969Journal Article20210908The notions of (transitive, commutative, antisymmetric) bordered GE-algebras are introduced,<br />and their properties are investigated. Relations between a commutative bordered GE-algebra and an<br />antisymmetric bordered GE-algebra are considered, and also relations between a commutative bordered<br />GE-algebra and a transitive bordered GE-algebra are discussed. Relations between a bordered GE-algebra and a bounded Hilbert algebra are stated, and the conditions under which every bordered GE-algebra (resp., bounded Hilbert algebra) can be a bounded Hilbert algebra (resp., bordered GE-algebra) are found. The concept of duplex bordered GE-algebras is introduced, and its properties are investigated. Relations between an antisymmetric bordered GE-algebra and a duplex bordered GE-algebra are discussed, and the conditions under which an antisymmetric bordered GE-algebra can be a duplex GE-algebra are established. A characterization of a duplex bordered GE-algebra is provided. A new bordered GE-algebra called cross bordered GE-algebra which is wider than duplex bordered GE-algebra is introduced, and its properties are investigated. Relations between a duplex bordered GE-algebra and a cross bordered GE-algebra are considered.https://jas.shahroodut.ac.ir/article_2834_d6c60e41844c3533f73a16ed6893470f.pdf