ABSTRACT. Suppose M is a hyperfinite von Neumann algebra with a tracial state φ and {a1, . . . , an} is a set of self-adjoint generators for M. We calculate δ0(a1, . . . , an), the modified free entropy dimension of {a1, . . . , an}. Moreover we show that δ0(a1, . . . , an) depends only on M and φ. Consequently δ0(a1, . . . , an) is independent of the choice of generators for M . In the course ...

One of the many equivalent formulation Köthe's conjecture is assertion that there exists no unital ring which contains two nil right ideals whose sum not nil. We discuss several consequences an observation if Koethe fails then a counterexample in form countable local subring suitable self-injective prime von Neumann regular ring.

We give two proofs of a conjecture of Neumann [N1] that a reduced algebraic plane curve is regular at infinity if and only if its link at infinity is a regular toral link. This conjecture has also been proved by Ha H. V. [H] using Lojasiewicz numbers at infinity. Our first proof uses the polar invariant and the second proof uses linear systems of plane curve singularities. The second approach a...