Browsing by Author "Öner, T."

Now showing 1 - 5 of 5

Another View of BZ-Algebras
(University of Guilan, 2025) Öner, T.; Katican, T.; Borumand Saeid, A.B.
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 SBZ-subalgebras, 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 SBZ-algebra. 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. © 2025 University of Guilan.
The Characterization of Nelson Algebras by Sheffer Stroke
(Sciendo, 2025) Öner, T.; Katican, T.; Borumand Saeid, A.B.
In this study, Sheffer stroke Nelson algebras (briefly, s-Nelson algebras), (ultra) ideals, quasi-subalgebras, quotient sets, and fuzzy structures on these algebraic structures are introduced. The relationships between s-Nelson and Nelson algebras are analyzed. It is also shown that an s-Nelson algebra is a bounded distributive modular lattice, and the family of all ideals forms a complete distributive modular lattice. A congruence relation on an s-Nelson algebra is determined by an ideal and quotient s-Nelson algebras are constructed by this congruence relation. Finally, it is indicated that a quotient s-Nelson algebra constructed by the ultra ideal is totally ordered and that the cardinality of the quotient is less than or equal to 2. © 2025 Tahsin Oner et al., published by Ovidius University of Constanta.
Neutrosophic N−ideals on Sheffer Stroke Bck-Algebras
(The Indonesian Mathematical Society, 2023) Öner, T.; Katican T.; Rezaei, A.
In this study, a neutrosophic N−subalgebra and neutrosophic N−ideal of a Sheffer stroke BCK-algebras are defined. It is shown that the level-set of a neutrosophic N−subalgebra (ideal) of a Sheffer stroke BCK-algebra is a subalgebra (ideal) of this algebra and vice versa. Then we present that the family of all neutrosophic N−subalgebras of a Sheffer stroke BCK-algebra forms a complete distributive modular lattice and that every neutrosophic N−ideal of a Sheffer stroke BCK-algebra is the neutrosophic N−subalgebra but the inverse does not usually hold. Also, relationships between neutrosophic N−ideals of Sheffer stroke BCK-algebras and homomorphisms are analyzed. Finally, we determine special subsets of a Sheffer stroke BCK-algebra by means of N−functions on this algebraic structure and examine the cases in which these subsets are its ideals. © 2023 The Author(s).
Citation - WoS: 1
Citation - Scopus: 3
On Ideals of Sheffer Stroke Up-Algebras
(Taru Publications, 2023) Öner, T.; Katıcan Tuğçe
The goal of the study is to introduce SUP-ideals on Sheffer Stroke UP-algebras (briefly, SUP-algebra) and its properties. We define SUP-ideals of SUP-algebras and then prove some properties. By describing a congruence relation on a SUP-algebra by the SUP-ideal, it is shown that the quotient set defined by the congruence relation is a SUP-algebra. Finally, SUP-homomorphisms on SUP-algebras are determined and the relationships between SUP-ideals of SUP-algebras are examined by means of the SUP-homomorphisms. © 2023, Taru Publications. All rights reserved.
Citation - Scopus: 1
Sheffer Stroke R0−Algebras
(Yazd University, 2023) Katıcan Tuğçe; Öner, T.; Saeid, A.B.
The main objective of this study is to introduce Sheffer stroke R0−algebra (for short, SR0− algebra). Then it is stated that the axiom system of a Sheffer stroke R0−algebra is independent. It is indicated that every Sheffer stroke R0−algebra is R0−algebra but specific conditions are necessarily for the inverse. Afterward, various ideals of a Sheffer stroke R0−algebra are defined, a congruence relation on a Sheffer stroke R0−algebra is determined by the ideal and quotient Sheffer stroke R0−algebra is built via this congruence relation. It is proved that quotient Sheffer stroke R0−algebra constructed by a prime ideal of this algebra is totally ordered and the cardinality is less than or equals to 2. After all, important conclusions are obtained for totally ordered Sheffer stroke R0−algebras by applying various properties of prime ideals. © 2023 Yazd University.