Leavitt R-algebras over countable graphs embed into L2,R

For a commutative ring R   with unit we show that the Leavitt path algebra LR(E)LR(E) of a graph E   embeds into L2,RL2,R precisely when E is countable. Before proving this result we prove a generalised Cuntz–Krieger Uniqueness Theorem for Leavitt path algebras over R.