Associative rings satisfying the Engel condition

Authors:
D. M. Riley and Mark C. Wilson

Journal:
Proc. Amer. Math. Soc. **127** (1999), 973-976

MSC (1991):
Primary 16R40; Secondary 16W10, 17B60, 16U60

DOI:
https://doi.org/10.1090/S0002-9939-99-04643-2

MathSciNet review:
1473677

Full-text PDF

Abstract | References | Similar Articles | 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 35487-0350

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 60607-7045

Email:
wilson@math.auckland.ac.nz

DOI:
https://doi.org/10.1090/S0002-9939-99-04643-2

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 NSF-EPSCoR 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