a ring $r$ is a strongly clean ring if every element in $r$ is the sum of an idempotent and a unit that commutate. we construct some classes of strongly clean rings which have stable range one. it is shown that such cleanness of $2 imes 2$ matrices over commutative local rings is completely determined in terms of solvability of quadratic equations.

decreasing changes of climatic elements such as: daily precipitation, weekly precipitation, seasonal precipitation and annual precipitation can be toward to drought phenomena. the recognition it and planning for passing it, could be decreasing of disasters, because create of drought is slow but it effects is very damages. the aim of this paper is descriptive analyze and it type of research is a...

BACKGROUND AND AIMS In dioecious species male and female plants experience different selective pressures and often incur different reproductive costs. An increase in reproductive investment habitually results in a reduction of the resources available to other demands, such as vegetative growth. Tree-ring growth is an integrative measure that tracks vegetative investment through the plant's enti...

in this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring r such that, every regular matrix admits a diagonal power-reduction.

New recruits of the bluehead wrasse Thalassoma bifasciatum were censused and collected from nearshore reefs of Barbados, West Indies, every 2 weeks for 20 months. Their temporal coincidence with low salinity (<34 5) water during their pelagic larval stage was determined by comparing the otolith records of new recruits with conductivity and temperature records from a current meter moored 2 km of...

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...