The rings considered in this article are  commutative  with identity which admit at least two  nonzero annihilating ideals. Let $R$ be a ring. Let $mathbb{A}(R)$ denote the set of all annihilating ideals of $R$ and let $mathbb{A}(R)^{*} = mathbb{A}(R)backslash {(0)}$. The annihilating-ideal graph of $R$, denoted by $mathbb{AG}(R)$  is an undirected simple graph whose vertex set is $mathbb{A}(R...

In this paper the energy absorption capacity of stiffened circular composite tube is considered. The governing equations and dynamic equilibrium are first derived and then solved. Additionally, a finite element model of reinforced circular composite tube structure is modeled. At the following, the effects of various parameters such as structural geometry, number of rings and stingers on mechani...

Simple observations on diophantine definability over finite commutative rings lead to a characterization of those rings in terms of their diophantine behavior. A.M.S. Classification: 13M10, 11T06, 03G99.

Those linearly compact rings with identity having a simple group of units and a transsnitely nilpotent Jacobson radical are identiied. A consequence of this characterization is Cohen and Koh's classiication theorem for compact rings with identity having a simple group of units.

An R-module is called semi-endosimple if it has no proper fully invariant essential submodules. For a quasi-projective retractable module MR we show that M is finitely generated semi-endosimple if and only if the endomorphism ring of M is a finite direct sum of simple rings. For an arbitrary module M , conditions equivalent to the semi-endosimplicity of its quasi-injective hull are found. As co...