let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

the zero-divisor graph of a commutative ring r with respect to nilpotent elements is a simple undirected graph $gamma_n^*(r)$ with vertex set z_n(r)*, and two vertices x and y are adjacent if and only if xy is nilpotent and xy is nonzero, where z_n(r)={x in r: xy is nilpotent, for some y in r^*}. in this paper, we investigate the basic properties of $gamma_n^*(r)$. we discuss when it will be eu...

THiE problem of correcting the refractive error of an aphakic eye other than by prescribing the cumbersome cataract lenses still remains open, in spite of the excellent work done in this field by Ridley, and all its modifications. In search of a method which might combine greater safety for the patient with a simpler operative technique, an operation has been devised which consists in implantin...

use of the double ring infiltrometer to measure soil water infiltration in center pivot irrigation systems isn’t an accurate approach because the real conditions of infiltration under center pivot sprinklers is different from what happens in the double ring. in this study the infiltration parameters were evaluated in real conditions of a center pivot system. for this purpose a single ring with ...