Let ?: R0?R be a ring homomorphism and suppose that a and a0, respectively, are ideals of R and R0 such that is an Artinian ring. Let M and N be two finitely generated R-modules and suppose that (R0,m0) is a local ring. In this note we prove that the R-modules and are Artinian for all integers i and j, whenever and . Also we will show that if a is principal, then the R-modules and ...

Composite stiffened cylindrical shells are widely used as primary elements in aerospace structures. In the recent years, there has been a growing research interest in optimum design of composite stiffened cylindrical shell structures for stability under buckling load.  This paper focuses upon the development of an efficient optimization of ring-stringer stiffened cylindrical shell. The opti...

‎Let $D$ be an integral domain with quotient field $K$‎, ‎$E$ be a $K$-vector space‎, ‎$R = D propto E$ be the trivial extension of $D$ by $E$‎, ‎and $w$ be the so-called $w$-operation‎. ‎In this paper‎, ‎we show that‎ ‎$R$ is a $w$-FF ring if and only if $D$ is a $w$-FF domain; and‎ ‎in this case‎, ‎each $w$-flat $w$-ideal of $R$ is $w$-invertible.

introduction: the wilson disease is an autosomal recessive disease in which the liver, central nervous system, eyes, blood and other parts of the body involved. timely diagnosis and appropriate treatment of the disease requires awareness of the clinical presentations of this disease in children.methods: this case series study included 62 patients with wilson disease who admitted to children&apo...

An intramolecular palladium catalysed carbometalation followed by anion capture achieves construction of a model comprised of the A ring of Vitamin D oxygen analogues.

An integral domain $D$ is called a emph{locally GCD domain} if $D_{M}$ is aGCD domain for every maximal ideal $M$ of $D$. We study somering-theoretic properties of locally GCD domains. E.g., we show that $%D$ is a locally GCD domain if and only if $aDcap bD$ is locally principalfor all $0neq a,bin D$, and flat overrings of a locally GCD domain arelocally GCD. We also show that the t-class group...

‎Let $R$ be a $*$-prime ring with center‎ ‎$Z(R)$‎, ‎$d$ a non-zero $(sigma,tau)$-derivation of $R$ with associated‎ ‎automorphisms $sigma$ and $tau$ of $R$‎, ‎such that $sigma$‎, ‎$tau$‎ ‎and $d$ commute with $'*'$‎. ‎Suppose that $U$ is an ideal of $R$ such that $U^*=U$‎, ‎and $C_{sigma,tau}={cin‎ ‎R~|~csigma(x)=tau(x)c~mbox{for~all}~xin R}.$ In the present paper‎, ‎it is shown that if charac...

Let a,d be two elements in rings and a∥d the inverse of a along d. When exists, we obtain several characterizations for invertibility aa∥d−a∥da, which is related to expressed by certain functions suitable from center ring. On other hand, some equivalent conditions equality aa∥d=a∥da, as complement previous sense, are given means group inverses ring units, respectively. Then, results obtained ap...

Let $R$ be a ring, $n$ an non-negative integer and $d$ positive or $\infty$. A right $R$-module $M$ is called \emph{$(n,d)^*$-projective} if ${\rm Ext}^1_R(M, C)=0$ for every $n$-copresented $C$ of injective dimension $\leq d$; ring \emph{right $(n,d)$-cocoherent} with $id(C)\leq d$ $(n+1)$-copresented; $(n,d)$-cosemihereditary} whenever $0\rightarrow C\rightarrow E\rightarrow A\rightarrow 0$ e...