Let L be a lattice with the greatest element 1. Following concept of Radsupplemented modules, we define Rad-supplemented filters and will make an intensive investigate basic properties possible structures these filters.

‎In this work‎, ‎we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules‎. ‎Let $R$ be a commutative ring with‎ ‎identity‎. ‎We say that a non-zero submodule $N$ of an $R$-module $M$ is a‎ ‎emph{classical 2-absorbing secondary submodule} of $M$ ...

We call a module  essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i)  A non-zero module  is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii)  A non-zero module  is essentially retractable if and on...

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete...

We show experimentally that properly selected chord-wise flexibility can have a significant effect on the propulsive efficiency of two-dimensional flapping (heaving and pithing) foils, up to a 36% increase, compared to the efficiency of a rigid foil, with small loss in thrust. Two different foil kinematics are employed in the experiments: the first using simple harmonic heave and pitch motions;...

Radon is one of the most important radioactive gases.Radon emits alpha particles and ultimately,it can cause genetic disorders.There are many reports of carcinogenesis and its harmful effects.One way to get this gas into the body is by eating and drinking.In the meantime,milk is one of the most consuming foods that can be contaminated with radon.In this study, the concentration of radon gas was...

‎‎Let $R$ be a commutative ring with identity and let $M$ be an $R$-module‎. ‎We define the primary spectrum of $M$‎, ‎denoted by $mathcal{PS}(M)$‎, ‎to be the set of all primary submodules $Q$ of $M$ such that $(operatorname{rad}Q:M)=sqrt{(Q:M)}$‎. ‎In this paper‎, ‎we topologize $mathcal{PS}(M)$ with a topology having the Zariski topology on the prime spectrum $operatorname{Spec}(M)$ as a sub...