The characterization of Nelson algebras by Sheffer stroke

Abstract 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.