# Embedding of von Neumann algebras

Let $A$ and $B$ be two purely infinite von Neumann algebras. Under which conditions $A$ can be embedded in $B$? For example is it true that every infinite factor can be embedded into the another infinite factor?

• Thank you for the answer. By the phrase "absorbs tensorially" you mean that it is of the form $M \otimes B(H)$ for some M? – truebaran Nov 1 '16 at 21:38
• Yes (and in fact $M$is the original vna, so M is properly infinite if and only if $– Stuart White Nov 1 '16 at 22:54 • Yes (and in fact$M$is the original vna, so$M$is properly infinite if and only if$M\cong M\,\overline{\otimes}\,B(H)\$. – Stuart White Nov 1 '16 at 22:55