This paper consists of several new results about Length property of the module M. F-length of any Module comes from several concepts like Neotherian module and Artinian modules (Neo and Art) with comp- sition series. We proved that any Neo -module has submodule T and Neo -module is F-length. This implies that T also has F-length Property. Finally, some remarks, examples and definitions have been presented in this paper.

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Let R be a ring with identity and let M be a unitary left module over R. In this paper, we study direct summand (direct sum) of essentially small quasi-Dedekind module (essentially small quasi-Dedekind modules). Also, give the definition of essentially small quasi-Dedekind relative to a module with some examples. We give some of their basic properties and some examples that illustrate these properties.