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Another view of BZ-algebras | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 آذر 1403 | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.26251.1612 | ||
| نویسندگان | ||
| A. Borumand Saeid* 1؛ T. Oner2؛ T. Katican2 | ||
| 1University of Kerman | ||
| 2Department of Mathematics, Ege University, Izmir 35100, Turkey | ||
| 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 showed that a Cartesian product of two SBZ-algebras is a SBZ-algebra. After giving SBZideals and SBZ-subalgebras, it is proved that any SBZ-ideal of a SBZ-algebra is an ideal of this SBZ-algebra and vice versa, and that it is also a SBZ-subalgebra. Also, a congruence relation on a SBZ-algebra is determined by a SBZ-ideal and quotient of a SBZ-algebra by a congruence relation on this algebra is constructed. Thus, it is proved that the quotient of the SBZ-algebra is a SBZ-algebra. Furthermore, we define SBZ-homomorphisms between SBZ-algebras and state that a kernel of a SBZ-homomorphism is a SBZ-ideal and so a SBZ-subalgebra. Hence, a new SBZ-homomorphism is described by means of a kernel of a SBZ-homomorphism. Finally, we show that some properties are preserved under SBZhomomorphisms. | ||
| کلیدواژه‌ها | ||
| BZ-algebra؛ Sheffer stroke؛ congruence؛ SBZ-homomorphism | ||
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آمار تعداد مشاهده مقاله: 72 |
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