Ring isomorphisms of Murray--von Neumann algebras
Shavkat Ayupov, Karimbergen Kudaybergenov
TL;DR
This paper characterizes all ring isomorphisms between algebras of measurable operators associated with type II$_1$ von Neumann algebras, providing a comprehensive understanding of their algebraic structure.
Contribution
It offers a complete classification of ring isomorphisms for algebras of measurable operators in the type II$_1$ setting, a previously unresolved problem.
Findings
Complete description of ring isomorphisms for type II$_1$ algebras
Identification of structural invariants preserved under isomorphisms
Extension of known results to a broader class of von Neumann algebras
Abstract
We give a complete description of ring isomorphisms between algebras of measurable operators affiliated with von Neumann algebras of type II
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