Let  be a commutative  ring with identity , and  be a unitary (left) R-module. A proper submodule  of  is said to be quasi- small prime submodule  , if whenever   with  and , then either or . In this paper ,we give a comprehensive study of quasi- small prime submodules.

Let R be a commutative ring with identity, and W be a unital (left) R-module. In this paper we introduce and study the concept of a quasi-small prime modules as generalization of small prime modules.

Let R be a commutative ring with identity, and M be unital (left) R-module. In this paper we introduce and study the concept of small semiprime submodules as a generalization of semiprime submodules. We investigate some basis properties of small semiprime submodules and give some characterizations of them, especially for (finitely generated faithful) multiplication modules.

Let R be a commutative ring with an identity, and G be a unitary R-module. We say that an R-module G is small semiprime if (0 G ) is small Semiprime submodule of G. Equivalently, an R-module G is small semiprime iff ann ρ= vÄP for each proper small submodule ρ of G. We have given and demonstrated some of the characterizations and features of these types of modules in this paper.

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