An approach to singular modules by indeterminacy concept

Majid Mohammed Abed^{1, *}, Abdulsalam F. Talak¹, Firas N. Hameed²

¹ Department of Mathematics, College of Education for Pure Sciences, University Of Anbar, Anbar, Iraq

²Ministry of Education, General Directorate of Education in Anbar Governorate, Anbar, Iraq

Emails: majid_math@uoanbar.edu.iq; abd19u2007@uoanbar.edu.iq; fir19u2013@uoanbar.edu.iq

Abstract

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.

Keywords: Singular module; Free module Annihilator module; Neutrosophic ring; Neutrosophic submodule.