Another view of BZ-algebras

Document Type : Research Paper

Authors

1 University of Kerman

2 Department of Mathematics, Ege University, Izmir 35100, Turkey

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
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.

Keywords

Main Subjects

Journal of Algebra and Related Topics

Articles in Press, Accepted Manuscript
Available Online from 04 December 2024

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