Covering modules by proper submodules

Submodules of Secondary Modules

Pure Submodules of Multiplication Modules

The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication and idempotent. Various properties and characterizations of pure submodules of multiplication modules are consid...

The generalized total graph of modules respect to proper submodules over commutative rings.

Let $M$ be a module over a commutative ring $R$ and let $N$ be a proper submodule of $M$. The total graph of $M$ over $R$ with respect to $N$, denoted by $T(Gamma_{N}(M))$, have been introduced and studied in [2]. In this paper, A generalization of the total graph $T(Gamma_{N}(M))$, denoted by $T(Gamma_{N,I}(M))$ is presented, where $I$ is an ideal of $R$. It is the graph with all elements of $...

δ-Small Submodules and δ-Supplemented Modules

Similar Submodules and Coincidence Site Modules

We consider connections between similar sublattices and coincidence site lattices and, more generally, between similar submodules and coincidence site modules of general (free) Z-modules in R. In particular, we generalise results obtained by S. Glied and M. Baake on similarity and coincidence isometries of lattices and certain lattice-like modules called S-modules. An important result is that t...