Vol. 39, No. 1, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Semi-orthogonality in Rickart rings

Louis Melvin Herman

Vol. 39 (1971), No. 1, 179–186
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
Authors
Louis Melvin Herman