Vol. 17, No. 2, 1966

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Some new results on simple algebras

David Joseph Rodabaugh

Vol. 17 (1966), No. 2, 311–317
Abstract

This paper deals with the problem of proving that a simple algebra (finite dimensional) has an identity element. The main result is contained in the following theorem. Let A be a simple algebra (char. 2) in which (x,x,x) = 0 and x3 x = x2 x2. If M is a subset of A such that (A,M,A) = 0 and (M,A,A) (M,A) (A,A,M) M, then M = 0 or there is an identity element in A. This result is then used to prove the three following corollaries (char. 2): (1) A simple power associative algebra with all commutators in the nucleus has an identity; (2) A simple power associative algebra with all associators in the middle center has an identity; (3) A simple antiflexible algebra in which (x,x,x) = 0 and A+ is not nil has an identity.

Mathematical Subject Classification
Primary: 17.20
Milestones
Received: 29 June 1964
Revised: 2 December 1964
Published: 1 May 1966
Authors
David Joseph Rodabaugh