The characterization of Bitonic algebras by Sheffer stroke

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Document Type : Research Paper

Authors

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

2 Department of Mathematics, Faculty of Arts and Sciences, Izmir University of Economics, Balcova, Izmir, Turkiye.

3 Department of Mathematics, Faculty of Arts and Sciences, Yaşar University, Bornova, Izmir, Turkey.

4 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shadid Bahonar University of Kerman, Kerman, Iran.

Abstract

The main objective of this study is to characterize bitonic algebras by means of the Sheffer stroke and to investigate some properties of related structures. It is shown that every Sheffer stroke bitonic algebra is a bitonic algebra, while the converse holds under special conditions. It is also illustrated that every Sheffer stroke bitonic algebra is a SUP-algebra; however, the converse is not true in general. By introducing certain filters of Sheffer stroke bitonic algebras, a congruence relation is defined on these algebraic structures. Moreover, quotient Sheffer stroke bitonic algebras are constructed via this congruence relation. Finally, homomorphisms on Sheffer stroke bitonic algebras are described, and fundamental homomorphism theorems are proved for these structures.

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References

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Algebraic Structures and Their Applications

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