Sheffer Stroke Nelson Algebras

In this study, Sheffer stroke Nelson algebras (briefly, s-Nelson algebras), (ultra) ideals, quasi-subalgebras and quotient sets on these algebraic structures are introduced. The relationships between s-Nelson and Nelson algebras are analyzed. Also, it is shown that a s-Nelson algbera is a bounded distributive modular lattice, and the family of all ideals forms a complete distributive modular lattice. A congruence relation on s-Nelson algebra is determined by its ideal and quotient s-Nelson algebras are constructed by this congruence relation. Finally, it is indicated that a quotient s-Nelson algebra defined by the ultra ideal is totally ordered and that the cardinality of the quotient is less than or equals to 2.

Neutrosophic N-structures on Sheffer stroke BE-algebras

In this study, a neutrosophic N-subalgebra, a (implicative) neutrosophic N-filter, level sets of these neutrosophic N-structures and their properties are introduced on a Sheffer stroke BE-algebras (briefly, SBE-algebras). It is proved that the level set of neutrosophic N-subalgebras ((implicative) neutrosophic N-filter) of this algebra is the SBE-subalgebra ((implicative) SBE-filter) and vice versa. Then it is proved that the family of all neutrosophic N-subalgebras of a SBE-algebra forms a complete distributive modular lattice. We present relationships between upper sets and neutrosophic N-filters of this algebra. Also, it is given that every neutrosophic N-filter of a SBE-algebra is its neutrosophic N-subalgebra but the inverse is generally not true. It is demonstrated that a neutrosophic N-structure on a SBE-algebra defi ned by a (implicative) neutrosophic N-filter of another SBE-algebra and a surjective SBE-homomorphism is a (implicative) neutrosophic N-filter. We present relationships between a neutrosophic N-filter and an implicative neutrosophic N-filter of a SBE-algebra in detail. Finally, certain subsets of a SBE-algebra are determined by means of N-functions and some properties are examined.

Filters of strong Sheffer stroke non-associative MV-algebras

In this paper, at first we study strong Sheffer stroke NMV-algebra. For getting more results and some classification, the notions of filters and subalgebras are introduced and studied. Finally, by a congruence relation, we construct a quotient strong Sheffer stroke NMV-algebra and isomorphism theorems are proved.

Fuzzy filters of Sheffer stroke Hilbert algebras

The aim of this study is to introduce fuzzy filters of Sheffer stroke Hilbert algebra. After defining fuzzy filters of Sheffer stroke Hilbert algebra, it is shown that a quotient structure of this algebra is described by its fuzzy filter. In addition to this, the level filter of a Sheffer stroke Hilbert algebra is determined by its fuzzy filter. Some fuzzy filters of a Sheffer stroke Hilbert algebra are defined by a homomorphism. Normal and maximal fuzzy filters of a Sheffer stroke Hilbert algebra and the relation between them are presented. By giving the Cartesian product of fuzzy filters of a Sheffer stroke Hilbert algebra, various properties are examined.