An approach to singular modules by indeterminacy concept.

In this article, we characterize a singular module and present several new strong relationships with neutrosophic (NC) properties. Some properties and characterizations neutrosophic of singular modules are given. Also, different basic results about these modules are considered. Moreover; for a (R ∪ I)-module; if NC(M∪I) over NC(R∪I), then NC(Z(M∪I)) ≤ NC(M∪I). Any neutrosophic simple module is either nonsingular or singular. On the other hand, if NC(RUI) has no zero divisors then NC(Z(MUI)) = NC(T(MUI)) where NC(T(MUI)) is a neutrosophic torsion module. Finally, some definitions and properties of neutrosophic singular module have been presented in this article. [ABSTRACT FROM AUTHOR]