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Result.Math. Online First c 2008 Birkhauser Verlag Basel/Switzerland
 

Summary: Result.Math. Online First
c 2008 Birkh¨auser Verlag Basel/Switzerland
DOI 10.1007/s00025-008-0305-5 Results in Mathematics
On Commutativity of Semiperiodic Rings
Howard E. Bell and Adil Yaqub
Abstract. Let R be a ring with center Z, Jacobson radical J, and set N of all
nilpotent elements. Call R semiperiodic if for each x R\(J Z), there exist
positive integers m, n of opposite parity such that xn
- xm
N. We inves-
tigate commutativity of semiperiodic rings, and we provide noncommutative
examples.
Mathematics Subject Classification (2000). 16U80.
Keywords. Semiperiodic rings, commutativity, periodic rings, Chacron crite-
rion.
1. Introduction
Let R be a ring with center Z = Z(R), Jacobson radical J = J(R), and set
N = N(R) of all nilpotent elements; and let Z and Z+
denote the ring of integers
and the set of positive integers. Define R to be periodic if for each x R, there

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics