In the literature, Baer *-rings are called as the algebraic analogue of von Neumann alegars.
It is well-known that
Theorem. Every von-Neumann algebra is decomposed into a direct sum of the algebras of type $I$, type $II_1$ , type $II_{\infty}$ and type $III$.
What is last version of the above theorem that has been accomplished in Baer *-rings?
