Let R be a commutative ring with identity and M be a unitary R- module. We shall say that M is a primary multiplication module if every primary submodule of M is a multiplication submodule of M. Some of the properties of this concept will be investigated. The main results of this paper are, for modules M and N, we have M N and HomR (M, N) are primary multiplications R-modules under certain assumptions.

The main goal of this paper is to introduce and studya new concept named Ᵹ*-supplemented which can be considered as a generalization of W-supplemented modules and Ᵹ-hollow module. Also, we introduce a Ᵹ*-supplement submodule.Many relationshipsof Ᵹ*-supplemented modules are studied. Especially, we give characterizations of Ᵹ*-supplemented modules and relationship between this kind of modules and other kind modules for example every Ᵹ-hollow (Ᵹ-local) module is Ᵹ*-supplemented and by an example we show that the converse is not true.

Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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The duo module plays an important role in the module theory. Many researchers generalized this concept such as Ozcan AC, Hadi IMA and Ahmed MA. It is known that in a duo module, every submodule is fully invariant. This paper used the class of St-closed submodules to work out a module with the feature that all St-closed submodules are fully invariant. Such a module is called an Stc-duo module. This class of modules contains the duo module properly as well as the CL-duo module which was introduced by Ahmed MA. The behaviour of this new kind of module was considered and studied in detail,for instance, the hereditary property of the St-duo module was investigated, as the result; under certain conditions, every St-cl