  In this paper we describe the amalgamated free product of finite and
semifinite hyperfinite von Neumann algebras over atomic type I subalgebras. To
do this we extend the notions of free dimension and standard embeddings used in
the related results for finite von Neumann algebras to ones which work better
for the semifinite case. We also define classes R3 (of finite von Neumann
algebras) and R4 (of semifinite von Neumann algebras) which are closed under
such amalgamated free products.

Operator Algebras