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.
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 left R-module. A proper submodule H of an R-module G is called semiprime if whenever a ∈ R, y ∈ G, n ∈ Z
+ and any ∈ H, then ay ∈ H. We say that a properi submodule H of an R-module G is a weakly small semiprime, if whenever a ∈ R, y ∈ G, n∈Z
+, (y) is small in G and 0 ≠ any ∈ H, implies ay ∈ H. Many basic properties and characterizations of this type of submodule are given.
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