Abstract
Within this research, we will study the relationships between Neutrosophic torsionless cyclic -module and Neutrosophic quasi-Frobenius rings. Some implications yeld cyclic -module and hence Neutrosophic quasi-Frobenius ring have been presented. In addition we study the relations between isomorphic Neutrosophic Noetherian ring and Neutrosophic quasi-Frobenius (Q-F) ring. Additionally, we present an important relation between Neutrosophic torsionless cyclic module, projective module and Neutrosophic injective module which through we get an Q-F ring. Finally, we study some concepts such as; Neutrosophic hollow module, Neutrosophic local module and Neutrosophic simple module which its relationship to the quasi-Frobenius rings.
Keywords: Quasi-Frobenius rings, Noetherian rings, torsionless, cyclic module, Hollo Module.
