Journal of Algebra and Related Topics
Volume:1 Issue: 1, Summer 2013

Let R be a commutative ring and M be an R-module. We say that M is fully primary, if every proper submodule of M is primary. In this paper, we state some characterizations of fully primary modules. We also give some characterizations of rings over which every module is fully primary, and of those rings over which there exists a faithful fully primary module. Furthermore, we will introduce some variations of fully primary modules and consider similar questions about them.

Let R be a commutative ring and let M be an R-module. In this article, we introduce the concept of the Zariski socles of submodules of M and investigate their properties. Also we study modules with Noetherian second spectrum and obtain some related results.

Let A be a C∗-algebra and E be a left Hilbert A-module. In this paper we define a product on E that making it into a Banach algebra and show that under the certain conditions E is Arens regular. We also study the relationship between derivations of A and E.

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.

R-module. In this paper, we explore more properties of Max-injective modules and we study some conditions under which the maximal spectrum of M is a Max -spectral space for its Zariski topology.

Let A be an abelian topological group and B a trivial topological A -module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can be embedded in the second bilinear cohomology.