let $m$ be a right module over a ring $r$, $tau_m$ a preradical on $sigma[m]$, and$ninsigma[m]$. in this note we show that if $n_1, n_2in sigma[m]$ are two$tau_m$-lifting modules such that $n_i$ is $n_j$-projective ($i,j=1,2$), then $n=n_1oplusn_2$ is $tau_m$-lifting. we investigate when homomorphic image of a $tau_m$-lifting moduleis $tau_m$-lifting.

in this paper, we present algebroids and crossed modules of algebroids. we also define pullbackcrossed module of algebroids.

the author studies the $bf r$$g$-module $a$ such that $bf r$ is an associative ring‎, ‎a group $g$ has infinite section $p$-rank (or infinite 0-rank)‎, ‎$c_{g}(a)=1$‎, ‎and for every‎ ‎proper subgroup $h$ of infinite section $p$-rank (or infinite 0-rank respectively) the quotient module $a/c_{a}(h)$ is‎ ‎a finite $bf r$-module‎. ‎it is proved that if the group $g$ under‎ ‎consideration is local...

background: yazd waste stabilization pond facilities consist of three stabilization pond systems, module 1, module 2 and module 3 that awsp module 1 has started its operation. the existing facilities have had several problems in their operation. the objectives of this research were to evaluate the performance of stabilization ponds in wastewater treatment of the city of yazd, due to several pro...

let r be a commutative ring and m be an r-module. we say that m is fully primary, if every proper submodule of m is primary. in this paper, we state some characterizations of fully primary modules. we also give some characterizations of rings over which every module is fully primary, and of those rings over which there exists a faithful fully primary module. furthermore, we will introduce some ...

Background: Yazd waste stabilization pond facilities consist of three stabilization pond systems, module 1, module 2 and module 3 that AWSP module 1 has started its operation. The existing facilities have had several problems in their operation. The objectives of this research were to evaluate the performance of stabilization ponds in wastewater treatment of the city of Yazd, due to several pro...

In this paper we introduce the notions of G∗L-module and G∗L-module whichare two proper generalizations of δ-lifting modules. We give some characteriza tions and properties of these modules. We show that a G∗L-module decomposesinto a semisimple submodule M1 and a submodule M2 of M such that every non-zero submodule of M2 contains a non-zero δ-cosingular submodule.