Another view of BZ-algebras

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Ege University, Izmir, Turkey

2 Department of Mathematics, Izmir University of Economics, Izmir, Turkey

3 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

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.

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Main Subjects

References

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Journal of Algebra and Related Topics
Volume 13, Issue 2
December 2025
Pages 119-135

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