Torsion Theories for Finite Von Neumann Algebras

Torsion Theories for Algebras of Affiliated Operators of Finite Von Neumann Algebras

The dimension of any module over an algebra of affiliated operators U of a finite von Neumann algebra A is defined using a trace on A. All zero-dimensional U-modules constitute the torsion class of torsion theory (T,P). We show that every finitely generated U-module splits as the direct sum of torsion and torsion-free part. Moreover, we prove that the theory (T, P) coincides with the theory of ...

Dimension and Torsion Theories for a Class of Baer *-Rings

Many known results on finite von Neumann algebras are generalized, by purely algebraic proofs, to a certain class C of finite Baer *-rings. The results in this paper can also be viewed as a study of the properties of Baer *-rings in the class C. First, we show that a finitely generated module over a ring from the class C splits as a direct sum of a finitely generated projective module and a cer...

Various topological forms of Von Neumann regularity in Banach algebras

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Nonlinear $*$-Lie higher derivations on factor von Neumann algebras

Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation$D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$factor, a concrete characterization of $D$ is given.