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Summary: International Journal of Algebra, Vol. 2, 2008, no. 14, 649 - 657
Generalized J-Rings and Commutativity
Hazar Abu-Khuzam
Department of Mathematics
American University of Beirut, Lebanon
hazar@aub.edu.lb
Adil Yaqub
Department of Mathematics
University of California
Santa Barbara, CA 93106, USA
Abstract
A J-ring is a ring R with the property that for every x in R there exists an integer
n(x)>1 such that xx xn
=)(
, and a well-known theorem of Jacobson states that a J-
ring is necessarily commutative. With this as motivation, we define a generalized J-
ring to be a ring R with the property that for all x, y in R0 there exists integers
1)(,1)( >=>= ymmxnn such that mn
xyyx - is nilpotent, where R0 is a certain
subset of R. The commutativity behavior of such rings is considered.
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