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

The amalgamated free product of semifinite hyperfinite von Neumann algebras over atomic type I subalgebras