A ring $R$ with identity is called ``clean'' if $~$for every element $ain R$, there exist an idempotent $e$ and a unit $u$ in $R$ such that $a=u+e$. Let $C(R)$ denote the center of a ring $R$ and $g(x)$ be a polynomial in $C(R)[x]$. An element $rin R$ is called ``g(x)-clean'' if $r=u+s$ where $g(s)=0$ and $u$ is a unit of $R$ and, $R$ is $g(x)$-clean if every element is $g(x)$-clean. In this pa...

Let $R$ be an associative ring with unity. An element $x \in R$ is called $\mathbb{Z}G$-clean if $x=e+r$, where $e$ is an idempotent and $r$ is a $\mathbb{Z}G$-regular element in $R$. A ring $R$ is called $\mathbb{Z}G$-clean if every element of $R$ is $\mathbb{Z}G$-clean. In this paper, we show that in an abelian $\mathbb{Z}G$-regular ring $R$, the $Nil(R)$ is a two-sided ideal of $R$ and $\fra...

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objective(s): up to now, many researches have been performed to improve the antitumoral effect of melanoma differentiation-associated gene-7 (mda-7) protein. the purpose of our research was to construct 3 expression vectors producing mda-7 in fusion with rgd (arginine-glycine-aspartic acid) peptide and evaluate their expression.     materials and methods: mda-7 gene with two different rgd seque...

objective(s): the goal of this study was assessing the prophylactic effect of exercise and its role as an adjuvant therapy on level of cytokines involved in angiogenesis in estrogen-dependent breast cancer. materials and methods: forty female balb/c mice were randomly assigned to exercise-tumor-exercise (ete), exercise-tumor-rest (etr), rest-tumor-exercise (rte) and rest-tumor-rest (rtr) groups...

Let F, G and H be non-empty graphs. The notation F → (G,H) means that if any edge of F is colored by red or blue, then either the red subgraph of F con- tains a graph G or the blue subgraph of F contains a graph H. A graph F (without isolated vertices) is called a Ramsey (G,H)−minimal if F → (G,H) and for every e ∈ E(F), (F − e) 9 (G,H). The set of all Ramsey (G,H)−minimal graphs is denoted by ...