Vol. 36, No. 3, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Speciality of quadratic Jordan algebras

Kevin Mor McCrimmon

Vol. 36 (1971), No. 3, 761–773
Abstract

In this paper we extend to quadratic Jordan algebras certain results due to P. M. Cohn giving conditions under which a Jordan algebra is special, the most important of ihese being the Shirshov-Cohn Theorem that a Jordan algebra with two generators and no extreme radical is always special. We also prove that the free algebra on two generators x, y modulo polynomial relations p(x) = 0,q(y) = 0 is special, and by taking a particular p(x) we show that most of the properties of the Peirce decomposition of a Jordan algebra relative to a supplementary family of orthogonal idempotents follow immediately from the analogous properties of Peirce decompositions in associative algebras.

Mathematical Subject Classification 2000
Primary: 17C10
Milestones
Received: 30 June 1970
Published: 1 March 1971
Authors
Kevin Mor McCrimmon