Let $R$ be a commutative ring and $M$ be an $R$-module with $T(M)$ as subset, the set of torsion elements. The total graph of the module denoted by $T(Gamma(M))$, is the (undirected) graph with all elements of $M$ as vertices, and for distinct elements $n,m in M$, the vertices $n$ and $m$ are adjacent if and only if $n+m in T(M)$. In this paper we study the domination number of $T(Gamma(M))$ a...

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...

Uterine rupture often occurs in the third trimester of pregnancy or during labor. Its occurrence in early pregnancy and in the absence of any predisposing factors is very rare. Untimely diagnosis and a low index of suspicion could be life-threatening. Here we report the case of a 29-year-old woman with a history of two previous cesarean sections. An ultrasound report revealed a dead fetus in th...

in this paper, we study the arens regularity properties of module actions and we extend some proposition from baker, dales, lau and others into general situations. we establish some relationships between the topological centers of module actions and factorization properties of them with some results in group algebras. in 1951 arens shows that the second dual of banach algebra endowed with the e...

we state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. in particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. also we show that if m is an strong comultiplicati...

the class of ads modules with the sip (briefly‎, ‎$sa$-modules) is studied‎. ‎various conditions for a module to be $sa$-module are given‎. ‎it is proved that for a quasi-continuous module $m$‎, ‎$m$ is a uc-module if and only if $m$ is an $sa$-module‎. ‎also‎, ‎it is proved that the direct sum of two $sa$-modules as $r$-modules is an $sa$-module when $r$ is the sum of the annihilators of these...

let $r$ be a commutative noetherian ring with non-zero identity and $fa$ an ideal of $r$. let $m$ be a finite $r$--module of finite projective dimension and $n$ an arbitrary finite $r$--module. we characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(m,n)$ in certain serre subcategories of the category of modules from upper bounds. we define and study the properti...

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.