In this work, we introduce $H^*$-condition on the set of submodules of a module. Let $M$ be a module. We say $M$ satisfies $H^*$ provided that for every submodule $N$ of $M$, there is a direct summand$D$ of $M$ such that $(N+D)/N$ and $(N+D)/D$ are cosingular. We show that over a right perfect right $GV$-ring,a homomorphic image of a $H^*$ duo module satisfies $H^*$.

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a charac...

Abstract. Let (R,P) be a Noetherian unique factorization do-main (UFD) and M be a finitely generated R-module. Let I(M)be the first nonzero Fitting ideal of M and the order of M, denotedord_R(M), be the largest integer n such that I(M) ⊆ P^n. In thispaper, we show that if M is a module of order one, then either Mis isomorphic with direct sum of a free module and a cyclic moduleor M is isomorphi...

Each object-oriented programming language proposes various grouping mechanisms to bundle interacting classes (i.e., packages, modules, selector namespaces, etc). To understand this diversity and to compare the different approaches, a common foundation is needed. In this paper we present a simple module calculus consisting of a small set of operators over environments and modules. Using these op...

in this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric connes amenability. we determine symmetric module amenability and symmetric connes amenability of some concrete banach algebras. indeed, it is shown that $ell^1(s)$ is  a symmetric $ell^1(e)$-module amenable if and only if $s$ is amenable, where $s$ is an inverse semigroup with subsemigr...

In this paper, small-signal modeling and robust controller design for multi-module parallel soft-switching mode rectifiers (SSMRs) are presented. First, a single-phase boost-type SSMR is formed from the traditional boost-type switching mode rectifier (SMR) with auxiliary resonant branch to achieve zero-voltage-transition (ZVT) soft switching for the main and auxiliary switches. Based on the pro...

the notions of quasi-prime submodules and developed  zariski topology was introduced by the present authors in cite{ah10}. in this paper we use these notions to define a scheme. for an $r$-module $m$, let $x:={qin qspec(m) mid (q:_r m)inspec(r)}$. it is proved that $(x, mathcal{o}_x)$ is a locally ringed space. we study the morphism of locally ringed spaces induced by $r$-homomorphism $mrightar...

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 ...

Our general goal is to provide a semantic foundation for the specification of concurrent and distributed object systems. We use Troll, a formal object-oriented language, for system specification. It is now widely accepted that object classes are unsuitable modularisation units when it comes to dealing with very large systems. An intermediate concept between the system and the objects is needed ...

A language for programming-in-the-large should support architectural descriptions of an entire product line. The evaluation of programs-in-the-large should generate the architecture of individual products and should link implementations-in-the-small to form an executable product. The Standard ML (SML) module language 20] could serve this task, but it is not referentially transparent. Furthermor...