Vol. 74, No. 1, 1978

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
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Three dimensional homogeneous algebras

James A. MacDougall and Lowell G. Sweet

Vol. 74 (1978), No. 1, 153–162
Abstract

An algebra A is homogeneous if its automorphism group acts transitively on the set of one dimensional subspaces of A. In this paper the structure of all three dimensional homogeneous algebra is determined. These fall into three classes: (1) truncated quaternion algebras over formally real Pythagorean fields; (2) an algebra over GF(2) in whlch x2 = x for all x in A, and (3) two algebras over GF(2) which are generated by each of their nonzero elements. The automorphism group is determined in each case.

Mathematical Subject Classification 2000
Primary: 17A99
Milestones
Received: 1 February 1977
Revised: 21 July 1977
Published: 1 January 1978
Authors
James A. MacDougall
Lowell G. Sweet