von Neumann algebra and matrices Is any matrix algebra regular in the sence of von Neuman? if yes could you tell me about any paper talk about this topic? 

A ring $R$ is Von Neumann regular if $\forall a\in R$ there exists $x\in R$ such that $a=axa$. 
We can show that the ring of all $n\times n$ matrices over a regular ring is regular. You can find the proof in: K.R. Goodearl , Von Neumann regular Rings, pag. 4.
