Vol. 70, No. 1, 1977

Recent Issues
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Vol. 317: 1  2
Vol. 316: 1  2
Vol. 315: 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
A commutativity study for periodic rings

Howard Edwin Bell

Vol. 70 (1977), No. 1, 29–36
Abstract

Putcha and Yaqub have proved that a ring R satisfying a polynomial identity of the form xy = ω(x,y), where ω(X,Y ) is a word different from XY , must have nil commutator ideal. Our first major theorem extends this result to the case where ω(X,Y ) varies with x and y, with the restriction that all ω(X,Y ) have length at least three and are not of the form XnY or XY n. Further restrictions on the ω(X,Y ) are then shown to yield commutativity of R; among these is a semigroup condition of Tamura, Putcha, and Weissglass—sepecifically, that each ω(X,Y ) begins with Y and has degree at least 2 in X. The final theorem establishes commutativity of rings R satisfying xy = yxs, where s = s(x,y) is an element in the center of the subring generated by x and y. All rings considered are either periodic by hypothesis or turn out to be periodic in the course of the investigation.

Mathematical Subject Classification
Primary: 16A70, 16A70
Milestones
Received: 9 December 1976
Revised: 3 March 1977
Published: 1 May 1977
Authors
Howard Edwin Bell