A Kurosh-type theorem for type II1 factors

We prove a Kurosh-type theorem for free-product type II1 factors. In particular, if M = LF2⊗ℛ, then the free-product type II1 factors M∗⋯∗M are all prime and pairwise nonisomorphic. We also study the case of crossed-product type II1 factors. This paper is a continuation of our previous papers, where the structure of (tensor products of) word-hyperbolic group type II1 factors was studied.