摘要
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.
延伸閱讀
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