S-Semiprime Submodules and S -Reduced Modules

S-pure Submodules

Purity in module categories and its different generalizations have been present in the literature since the 1960s. Apart from its special role in module theory, the importance of purity increased during the last two decades through the developments of model theory and the study of locally finitely presented categories (e.g., [2, 6]). In the module theory context, that will be our framework, a p...

On graded almost semiprime submodules

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring with a non-zero identity and $M$ be a graded $R$-module. In this article, we introduce the concept of graded almost semiprime submodules. Also, we investigate some basic properties of graded almost semiprime and graded weakly semiprime submodules and give some characterizations of them.

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...

Orthogonal Spectra and S-modules

There are several symmetric monoidal categories of “spectra” that are model categories with homotopy categories equivalent to the stable homotopy category. The most highly developed, and the first to be made rigorous, is the category M = MS of S-modules of [1]. Its objects are quite complicated, but the complication encodes computationally important information. A second such category is the ca...