Abstract In previous research, a concept was presented f –small submodules A submodule L of an R-module W is named if L+X=W and W/X are small-singular, then X=W. this work, we present new concept, namely –hollow modules, -hollow every in -small submodule. This expansion Hollow modules. Some characteristics given to their relationship few the concepts comparability between them examined.

Let R be ring and M a right R-module. This article introduces the concept of τ −⊕-supplemented modules as follows: Given a hereditary torsion theory in Mod-R with associated torsion functor τ we say that a module M is τ −⊕-supplemented when for every submodule N of M there exists a direct summand K of M such that M = N +K and N ∩K is τ−torsion, and M is called completely τ −⊕-supplemented if ev...

1. [10 points] Determine whether the following statements are true or false (you have to include proofs/counterexamples): (a) Let R be an integral domain, F – a free R-module of finite rank, and M – a torsion R-module. Then there is no injective homomorphism from F to M . Solution: True. Suppose there was an injective homomorpism φ : F → M . Then let N = φ(F ); N is a submodule of M , and there...

This paper focuses on the engineering trade-offs in designing capacitor voltage balancing schemes for modular multilevel converters (MMC) HVDC: regulation performance and switching loss. MMC is driven by the on/off switch operation of numerous submodules and the key design concern is balancing submodule capacitor voltages minimizing switching transition among submodules because it represents th...

BRST-resolution is studied for the principally graded Wakimoto module of ŝl2 recently found in [9]. The submodule structure is completely determined and irreducible representations can be obtained as the zero-th cohomology group. e-mail:[email protected]

‎A module $M$ is lifting if and only if $M$ is amply supplemented and‎ ‎every coclosed submodule of $M$ is a direct summand‎. ‎In this paper‎, ‎we are‎ ‎interested in a generalization of lifting modules by removing the condition‎"‎amply supplemented‎" ‎and just focus on modules such that every non-cosingular‎ ‎submodule of them is a summand‎. ‎We call these modules NS‎. ‎We investigate some gen...

The cross-characteristic permutation modules for the actions of the finite classical groups on singular 1-spaces of their natural modules are studied. The composition factors and submodule lattices are determined.

Altered brain morphometry has been widely acknowledged in chronic pain, and recent studies have implicated altered network dynamics, as opposed to properties of individual brain regions, in supporting persistent pain. Structural covariance analysis determines the inter-regional association in morphological metrics, such as gray matter volume, and such structural associations may be altered in c...

We provide an upper bound of the dimension of the maximal projective submodule of the Lie module of the symmetric group of n letters in prime characteristic p, where n = pk with p k.