Let Λ be a commutative local uniserial ring of length n, p a generator of the maximal ideal, and k the radical factor field. The pairs (B, A) where B is a finitely generated Λ-module and A ⊆ B a submodule of B such that pmA = 0 form the objects in the category Sm(Λ). We show that in case m = 2 the categories Sm(Λ) are in fact quite similar to each other: If also ∆ is a commutative local uniseri...

The purpose of this paper is to introduce new concepts in a module  over ring , the first one called e*- small essential submodule, which generalization second concept called e*-radical submodule radical and last e* - hollow module. We will prove some properties all these concepts.

In this paper we investigate decompositions of submodules in modules over a Proufer domain into intersections of quasi-primary and classical quasi-primary submodules. In particular, existence and uniqueness of quasi-primary decompositions in modules over a Proufer domain of finite character are proved. Proufer domain; primary submodule; quasi-primary submodule; classical quasi-primary; decompo...

We determine the blocks of the Brauer algebra in characteristic zero. We also give information on the submodule structure of standard modules for this algebra.

We prove that two dual operator algebras are weak Morita equivalent in the sense of [4] if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weakcontinuous on appropriate morphism spaces. Moreover, in a fashion similar to the operator algebra case we can characterize such functors as the module normal Haagerup tensor product ...

Let $R$ be a commutative ring with identity. The purpose of this paper is to introduce and study two classes of modules over $R$, called $mbox{Max}$-injective and $mbox{Max}$-strongly top modules and explore some of their basic properties. Our concern is to extend some properties of $X$-injective and strongly top modules to these classes of modules and obtain some related results.

Let $G$ be a group with identity $e$, $R$ commutative $G$-graded ring unity $1$ and $M$ unital $R$-module. In this article, we introduce the concept of graded $1$-absorbing prime submodule. A proper $R$-submodule $N$ is said to if for all non-unit homogeneous elements $x, y$ element $m$ $xym\in N$, either $xy\in (N :_{R} M)$ or $m\in N$. We show that new generalization submodules at same time i...

This paper is a licentiate compilation-thesis that aims to bring clarity to the dimensioning aspects and limiting factors of modular multilevel converters. The dc-capacitor in each submodule is a driving factor for the size and weight of the converter. This means that it is important to distribute the stored energy evenly among all submodule capacitors. Typically, an increased switching frequen...

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 ...

the generalized principal ideal theorem is one of the cornerstones of dimension theory for noetherian rings. for an r-module m, we identify certain submodules of m that play a role analogous to that of prime ideals in the ring r. using this definition, we extend the generalized principal ideal theorem to modules.