BORDERED GE-ALGEBRAS

Document Type : Original Manuscript

Authors

1 Department of Mathematics, GITAM(Deemed to be University), P.O. Box 502329, Telangana State, India

2 Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, P.O. Box 02040, Adıyaman, Turkey

3 Department of Mathematics Education, Gyeongsang National University, P.O. Box 52828, Jinju, Korea.

Abstract

The notions of (transitive, commutative, antisymmetric) bordered GE-algebras are introduced,
and their properties are investigated. Relations between a commutative bordered GE-algebra and an
antisymmetric bordered GE-algebra are considered, and also relations between a commutative bordered
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.

Keywords

References

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Journal of Algebraic Systems
Volume 12, Issue 1
September 2024
Pages 43-58

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