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...

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 ...

‎let $r$ be a ring with involution $*$‎. ‎an additive mapping $t:rto r$ is called a left(respectively right) centralizer if $t(xy)=t(x)y$ (respectively $t(xy)=xt(y)$) for all $x,yin r$‎. ‎the purpose of this paper is to examine the commutativity of prime rings with involution satisfying certain identities involving left centralizers.

6-methyl-2-phenyl-7h-oxazolo [3,2-b] [1,2,4] triazine (1) undersent ting transformation on treatment with ammonia and primary amines to afford the corresponding imidazol [1,2-b][1,2,4] triazine (2). treatment of (1) with hydrazine hydrate gave the corresponding 3-aryl-4h-1,2,4- triazino [4,3-b][1,2,4] triazin-8 (1h)-one (3).

in this paper, we define and study the notion of the real-valued functions on a frame $l$. we show that $f(l) $, consisting of all frame homomorphisms from the power set of $mathbb{r}$ to a frame $ l$, is an $f$-ring, as a generalization of all functions from a set $x$ into $mathbb r$. also, we show that $f(l) $ is isomorphic to a sub-$f$-ring of $mathcal{r}(l)$, the ring of real-valued continu...

abstract determining saturated hydraulic conductivity (ks) is one of the important soil characteristics that its estimation is important in soil and water studies. there are several methods for estimating ks in unsaturated conditions. these methods include the inversed-auger-hole method, the double-ring infiltrometer and the single-ring pressure infiltrometer. the measurement of ks by these met...

in this paper, we introduce the new notion of strongly j-clean rings associatedwith polynomial identity g(x) = 0, as a generalization of strongly j-clean rings. we denotestrongly j-clean rings associated with polynomial identity g(x) = 0 by strongly g(x)-j-cleanrings. next, we investigate some properties of strongly g(x)-j-clean.

in this paper we prove that each element of any regular baer ring is a sum of two units if no factor ring of r is isomorphic to z_2 and we characterize regular baer rings with unit sum numbers $omega$ and $infty$. then as an application, we discuss the unit sum number of some classes of group rings.