Generalized periodic rings

Howard E. Bell and Adil Yaqub

International Journal of Mathematics and Mathematical Sciences, 1996, vol. 19, 1-6

Abstract:

Let R be a ring, and let N and C denote the set of nilpotents and the center of R , respectively. R is called generalized periodic if for every x ∈ R \ ( N ⋃ C ) , there exist distinct positive integers m , n of opposite parity such that x n − x m ∈ N ⋂ C . We prove that a generalized periodic ring always has the set N of nilpotents forming an ideal in R . We also consider some conditions which imply the commutativity of a generalized periodic ring.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:941034

DOI: 10.1155/S0161171296000130

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