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.

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. ‎$r$ ...

Gage, J. C. (1970). Brit. J. industr. Med., 27, 1-18. The subacute inhalation toxicity of 109 industrial chemicals. The inhalation toxicity of 109 substances has been studied by exposing experimental animals to known concentrations in air for periods of about three weeks. The toxic properties of these substances are reviewed in relation to the effects of similar compounds on animals and on man....

Six sigma is a highly disciplined process that focuses on developing and delivering nearperfect products and services consistently. Six sigma is also a management stragety to use statistical tools and project work to achieve breakthrough profitability and quantum gains in quality. The steps in the six sigma process are Define, Measure, Analyse, Improve, Control or DMAIC for short (Kubiak T.M, B...

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...