Neutrosophic N −structures on Sheffer stroke Hilbert algebras

Abstract

In this study, a neutrosophic N −subalgebra and a level set of a neutrosophic N −structure are
defined on Sheffer stroke Hilbert algebras. By determining a subalgebra on Sheffer stroke Hilbert algebras, it is
proved that the level set of neutrosophic N −subalgebras on this algebra is its subalgebra and vice versa. It is
stated that the family of all neutrosophic N −subalgebras of a Sheffer stroke Hilbert algebra forms a complete
distributive lattice. Finally, a neutrosophic N −ideal of a Sheffer stroke Hilbert algebra is described and some
of properties are given. Also, it is shown that every neutrosophic N −ideal of a Sheffer stroke Hilbert algebra
is its neutrosophic N −subalgebra but the inverse is generally not valid