Semi-orthogonality in Rickart rings

Louis Melvin Herman

Vol. 39 (1971), No. 1, 179–186

DOI: 10.2140/pjm.1971.39.179

Abstract

This note initiates a study of the semi-orthogonality relation on the lattice of principal left ideals generated by idempotents of a Rickart ring. It will be seen that two left ideals in a von Neumann algebra are semi-orthogonal if and only if their unique generating projections are non-asymptotic. Connections between semi-orthogonality, dual modularity, von Neumann regularity, and algebraic equivalence will be established; those Rickart rings with a superabundance of semiorthogonal left ideals will be characterized.

Mathematical Subject Classification

Primary: 16A30

Milestones

Received: 23 October 1970

Published: 1 October 1971