The main aim of this paper is to show that an AB5 module whose small submodules have Krull dimension has a radical having Krull dimension. The proof uses the notion of dual Goldie dimension.

Let R be an integral domain and let Q denote the quotient field of R. We investigate the structure of R-submodules of Q that are Q-irreducible, or completely Q-irreducible. One of our goals is to describe the integral domains that admit a completely Q-irreducible ideal, or a nonzero Q-irreducible ideal. If R has a nonzero finitely generated Q-irreducible ideal, then R is quasilocal. If R is int...

The purpose of this paper is to initiate a new attack on Arveson’s resistant conjecture, that all graded submodules of the d-shift Hilbert module H are essentially normal. We introduce the stable division property for modules (and ideals): a normed module M over the ring of polynomials in d variables has the stable division property if it has a generating set {f1, . . . , fk} such that every h ...

let $r$ be a commutative ring with identity and let $m$ be an $r$-module. a proper submodule $p$ of $m$ is called strongly prime submodule if $(p + rx : m)ysubseteq p$ for $x, yin m$, implies that $xin p$ or $yin p$. in this paper, we study more properties of strongly prime submodules. it is shown that a finitely generated $r$-module $m$ is artinian if and only if $m$ is noetherian and every st...

The purpose of this paper is to introduce a new concept in module M over ring R, called e∗-essential submodule, which generalization an essential submodule. We will some examples and properties about such that, what the inverse image intersection submodules direct sum submodules. show relationship between submodule Noetherian R-module. Also we define e∗-closed with

The Modular Multilevel Matrix Converter (M3C) is an attractive topology for low-speed drives and DFIG applications. Both modularity scalability make the high-power medium-voltage systems. One of main challenges design implementation M3C control platform, which has to handle a high number submodules measured values. This paper introduces new platform including high-speed communication network be...

The target of this study is to observe some of the algebraic structures of a single valued neutrosophic set. So, we introduce the concept of a neutrosophic submodule of a given classical module and investigate some of the crucial properties and characterizations of the proposed concept.

In this work we study a realization of moduli spaces of framed quiver representations as Grassmannians of submodules devised by Markus Reineke. Obtained is a generalization of this construction to finite dimensional associative algebras and for quivers with oriented cycles over an arbitrary infinite field. As an application we get an explicit realization of fibers for the moduli space bundle ov...