Let $M_R$ be a non-zero‎ ‎module and ${mathcal F}‎: ‎sigma[M_R]times sigma[M_R]‎ ‎rightarrow$ Mod-$Bbb{Z}$ a bifunctor‎. ‎The‎ ‎$mathcal{F}$-reversibility of $M$ is defined by ${mathcal‎ ‎F}(X,Y)=0 Rightarrow {mathcal F}(Y,X)=0$ for all non-zero $X,Y$‎ ‎in $sigma[M_R]$‎. ‎Hom (resp‎. ‎Rej)-reversibility of $M$ is‎ ‎characterized in different ways‎. ‎Among other things‎, ‎it is shown‎ ‎th...

This paper provides a comprehensive overview of our Network Time Interface (NTI) M-Module, which facilitates high-accuracy time distribution in LAN-based distributed real-time systems. Built around our custom UTCSU VLSI chip, it hosts all the hardware support required for interval-based external clock synchronization: A high-resolution state-and rate-adjustable clock, local accuracy intervals, ...

M be a module. In this article we study δ–essential submodules as a dual of δ-small submodules of Zhou where δ = {N ∈ σ[M ] : Rej(N,M) = 0} and M = {N ∈ σ[M ] : N ¿ b N}, and also define μ-M–singular modules as modules N ∈ σ[M ] such that N ∼= K/L for some K ∈ σ[M ] and L is μ–essential in K. By M–M–singular modules and δ–M– singular modules a characterization of GCO–modules, and by FC–M–singul...

let d be a division ring with centre k and dim, d< ? a valuation on k and v a noninvariant extension of ? to d. we define the initial ramfication index of v over ?, ?(v/ ?) .let a be a valuation ring of o with maximal ideal m, and v , v ,…, v noninvariant extensions of w to d with valuation rings a , a ,…, a . if b= a , it is shown that the following conditions are equivalent: (i) b is a finite...

Dedicated to the memory of Maurice Auslander Given a ring we introduce the endocategory E M of a-module M. It is an abelian subcategory of Mod(?) where ? = End (M) op , and E M is constructed in such a way that it is the smallest abelian subcategory of Mod(?) containing M regarded in the natural way as a ?-module and all the endomorphisms of M induced by multiplication with an element from. The...

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...

The purpose of this paper is to further the study of weakly injective and weakly projective modules as a generalization of injective and projective modules. For a locally q.f.d. module M , there exists a module K ∈ σ[M ] such that K ⊕N is weakly injective in σ[M ], for any N ∈ σ[M ]. Similarly, if M is projective and right perfect in σ[M ], then there exists a module K ∈ σ[M ] such that K ⊕ N i...

Let $M$ be a module over a commutative ring $R$ and let $N$ be a proper submodule of $M$. The total graph of $M$ over $R$ with respect to $N$, denoted by $T(Gamma_{N}(M))$, have been introduced and studied in [2]. In this paper, A generalization of the total graph $T(Gamma_{N}(M))$, denoted by $T(Gamma_{N,I}(M))$ is presented, where $I$ is an ideal of $R$. It is the graph with all elements of $...

Recent interest in cube satellites over the last few years has created related interest in propulsion for small satellites. Cubesats, more than other satellites, are volume and power constrained, which pose significant challenges for implementation of cubesat propulsion systems. R-134a propellant systems can provide low cost and efficient propulsion for small impulse maneuvers, orbital maintena...