BORDERED GE-ALGEBRAS | ||
| Journal of Algebraic Systems | ||
| دوره 12، شماره 1، آذر 2024، صفحه 43-58 اصل مقاله (133.88 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11184.1558 | ||
| نویسندگان | ||
| Ravikumar Bandaru* 1؛ Mehmet Ali Ozturk2؛ Young Bae Jun3 | ||
| 1Department of Mathematics, GITAM(Deemed to be University), P.O. Box 502329, Telangana State, India | ||
| 2Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, P.O. Box 02040, Adıyaman, Turkey | ||
| 3Department of Mathematics Education, Gyeongsang National University, P.O. Box 52828, Jinju, Korea. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| (Commutative؛ transitive؛ antisymmetric) bordered GE-algebra؛ duplex bordered GE-algebra؛ cross bordered GE-algebra | ||
| مراجع | ||
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