Residuation Properties and Weakly Primary Elements in Lattice Modules

Weakly Prime Elements in Lattice Modules

As a generalization of the notion of prime element and semiprime element, we introduce the notion of weakly prime element and weakly semiprime element in lattice modules. Some characterization of weakly prime and weakly semiprime elements are obtained. Throughout this paper, L will be a lattice domain.

On weakly projective and weakly injective modules

The purpose of this paper is to further the study of weakly injective and weakly projective modules as a generalization of injective and projective modules. For a locally q.f.d. module M , there exists a module K ∈ σ[M ] such that K ⊕N is weakly injective in σ[M ], for any N ∈ σ[M ]. Similarly, if M is projective and right perfect in σ[M ], then there exists a module K ∈ σ[M ] such that K ⊕ N i...

On Weakly Co-Hopfian Modules

Dependent Lattice Random Elements

In this study, we first introduce the Banach lattice random elements and some of their properties. Then, using the order defined in Banach lattice space, we introduce and characterize the order negatively dependence Banach lattice random elements by the order defined in Banach lattice space. Finally, we obtain some limit theorems for the sequence of order negatively dependence Banach lattice ra...

On Semi-artinian Weakly Co-semisimple Modules

We show that every semi-artinian module which is contained in a direct sum of finitely presented modules in $si[M]$, is weakly co-semisimple if and only if it is regular in $si[M]$. As a consequence, we observe that every semi-artinian ring is regular in the sense of von Neumann if and only if its simple modules are $FP$-injective.