Let g be a semisimple complex Lie algebra and k ⊂ g be any algebraic subalgebra reductive in g. For any simple finite dimensional k-module V , we construct simple (g, k)-modules M with finite dimensional k-isotypic components such that V is a k-submodule of M and the Vogan norm of any simple k-submodule V ′ ⊂ M, V ′ 6≃ V , is greater than the Vogan norm of V . The (g, k)-modules M are subquotie...

A combination of crystallography, biochemistry, and gene expression analysis identifies the coactivator subcomplex Med8C/18/20 as a functionally distinct submodule of the Mediator head module. Med8C forms a conserved alpha-helix that tethers Med18/20 to the Mediator. Deletion of Med8C in vivo results in dissociation of Med18/20 from Mediator and in loss of transcription activity of extracts. De...

The Hardy space on the unit ball in C provides examples of a quasi-free, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n = 1 the submodule has finite codimension. In this note we show that this phenomenon can only occur for modules over domains in C and for finitely-connected domains only for Hardy-like spaces, the bundle shifts. M...

In this paper, we introduce the concept of a quasi-radical semi prime submodule. Throughout work, assume that is commutative ring with identity and left unitary R- module. A proper submodule called (for short Q-rad-semiprime), if for , ,and then . Where intersection all submodules

A module M is called ?-?ss-supplemented if every submodule X of has a ?ss-supplement Y in which direct summand such that + = and ? Soc? (Y) where Soc?(Y) the sum simple ?-small submodules Y? for some M. Moreover, completely ?-?ss-supplemented. Thus, we present two new types algebraic structures are stronger than ?-D11 ?-D+11-modules, respectively. In this paper investigate basic properties, dec...

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.

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...

We study the space of functions on a finite-dimensional vector space over a field of odd order as a module for a symplectic group. We construct a basis of this module with the following special properties. Each submodule generated by a single basis element under the symplectic group action is spanned as a vector space by a subset of the basis and has a unique maximal submodule. From these prope...

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...