Some Characterizations of Modules via Essentially Small Submodules

δ-Small Submodules and δ-Supplemented Modules

Modules Whose Small Submodules Have Krull Dimension

The main aim of this paper is to show that an AB5 module whose small submodules have Krull dimension has a radical having Krull dimension. The proof uses the notion of dual Goldie dimension.

Research Article -Small Submodules and -Supplemented Modules

Some applications of the product of submodules in multiplication modules

Let R be a commutative ring with identity. Let N and K be two submodules of a multiplication R-module M. Then N=IM and K=JM for some ideals I and J of R. The product of N and K denoted by NK is defined by NK=IJM. In this paper we characterize some particular cases of multiplication modules by using the product of submodules.

Submodules of Secondary Modules