Vol. 37, No. 3, 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
Linear semiprime (p; q) radicals

Gary L. Musser

Vol. 37 (1971), No. 3, 749–757
Abstract

This paper introduces McKnight’s (p;q)-regularity and (p;q) radicals, a collection of radicals which contains the Jacobson radical and the radicals of regularity and strong regularity among its members. The linear semiprime (p;q) radicals are classified canonically and, as a result of this classification, these radicals can be distinguished by the fields GF(p) and are shown to form a lattice. The semiprime (p;q) radicals are found to be hereditary and the linear semiprime (p;q) radical of a complete matrix ring of a ring R is determined to be the complete matrix ring over the (p;q) radical of R. More generally, the (p;q) radical of a complete matrix ring over R is contained in the matrix ring over the (p;q) radical of R for all (p;q) radicals.

Mathematical Subject Classification
Primary: 16A21
Milestones
Received: 6 November 1969
Revised: 23 October 1970
Published: 1 June 1971
Authors
Gary L. Musser