The classification of type II1 factors (of discrete groups) was initiated by Murray and von Neumann [MvN] who distinguished the hyperfinite type II1 factor R from the group factor LFr of the free group Fr on r ≥ 2 generators. Thirty years later, Connes [Co2] proved uniqueness of the injective type II1 factor. Thus, the group factor LΓ of an ICC amenable group Γ is isomorphic to the hyperfinite ...

In [Oz], Ozawa obtained analogues of the Kurosh subgroup theorem (and its consequences) in the setting of free products of semiexact II1 factors with respect to the canonical tracial states. In particular he was able to prove a certain unique-factorization theorem that distinquishes, for example, the n-various L(F∞) ∗ (L(F∞)⊗ R) . The paper was a continuation of the joint work [OP] with Popa th...

By a near-ring we mean a right near-ring. J 0 , the right Jacobson radical of type 0, was introduced for near-rings by the first and second authors. In this paper properties of the radical J 0 are studied. It is shown that J 0 is a Kurosh-Amitsur radical KA-radical in the variety of all near-rings R, in which the constant part Rc of R is an ideal of R. So unlike the left Jacobson radicals of ty...

A modular semilattice is a semilattice S in which w > a A ft implies that there exist i,jeS such that x > a. y > b and x A y = x A w. This is equivalent to modularity in a lattice and in the semilattice of ideals of the semilattice, and the condition implies the Kurosh-Ore replacement property for irreducible elements in a semilattice. The main results provide extensions of the classical charac...