Associative rings satisfying the Engel condition
Authors:
D. M. Riley and Mark C. Wilson
Journal:
Proc. Amer. Math. Soc. 127 (1999), 973976
MSC (1991):
Primary 16R40; Secondary 16W10, 17B60, 16U60
MathSciNet review:
1473677
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: Let be a commutative ring, and let be an associative algebra generated by elements . We show that if satisfies the Engel condition of degree , then is upper Lie nilpotent of class bounded by a function that depends only on and . We deduce that the Engel condition in an arbitrary associative ring is inherited by its group of units, and implies a semigroup identity.
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Additional Information
D. M. Riley
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 354870350
Email:
driley@gp.as.ua.edu
Mark C. Wilson
Affiliation:
Department of Mathematics, University of Auckland, Private Bag 92019 Auckland, New Zealand
Address at time of publication:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois 606077045
Email:
wilson@math.auckland.ac.nz
DOI:
http://dx.doi.org/10.1090/S0002993999046432
PII:
S 00029939(99)046432
Keywords:
Engel identity,
Lie nilpotent,
strongly Lie nilpotent,
upper Lie nilpotent,
nonmatrix
Received by editor(s):
March 20, 1997
Received by editor(s) in revised form:
April 15, 1997, and July 29, 1997
Additional Notes:
The first author received support from NSFEPSCoR in Alabama and the University of Alabama Research Advisory Committee.
The second author was supported by a NZST Postdoctoral Fellowship.
Communicated by:
Ken Goodearl
Article copyright:
© Copyright 1999
American Mathematical Society
