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Another view of BZ-algebras | ||
| Journal of Algebra and Related Topics | ||
| دوره 13، شماره 2، اسفند 2025، صفحه 119-135 اصل مقاله (174.88 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.26251.1612 | ||
| نویسندگان | ||
| T. Oner1؛ T. Katican2؛ A. Borumand Saeid* 3 | ||
| 1Department of Mathematics, Faculty of Science, Ege University, Izmir, Turkey | ||
| 2Department of Mathematics, Izmir University of Economics, Izmir, Turkey | ||
| 3Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| چکیده | ||
| In this work, Sheffer stroke BZ-algebra (briefly, SBZ-algebra) is introduced and its properties are examined. Then a partial order is defined on SBZ-algebras. It is shown that a Cartesian product of two SBZ-algebras is an SBZ-algebra. After giving SBZ-ideals and SBZsubalgebras, it is proved that any SBZ-ideal of an SBZ-algebra is an ideal of this SBZ-algebra and vice versa, and that it is also an SBZ-subalgebra. Also, a congruence relation on an SBZ-algebra is determined by an SBZ-ideal, and the quotient of an SBZ-algebra by a congruence relation on this algebra is constructed. Thus, it is proved that the quotient of the SBZ-algebra is an SBZalgebra. Furthermore, we define SBZ-homomorphisms between SBZ-algebras and state that the kernel of an SBZ-homomorphism is an SBZ-ideal and so an SBZ-subalgebra. Hence, a new SBZ-homomorphism is described by means of the kernel of an SBZ-homomorphism. Finally, we show that some properties are preserved under SBZ-homomorphisms. | ||
| کلیدواژهها | ||
| BZ-algebra؛ Sheffer stroke؛ Congruence؛ SBZ-homomorphism | ||
| مراجع | ||
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