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On generalized periodic-like rings. (English) Zbl 1140.16013
Summary: Let \(R\) be a ring with center \(Z\), Jacobson radical \(J\), and set of nilpotent elements \(N\). Call \(R\) generalized periodic-like if for all \(x\in R\setminus(N\cup J\cup Z)\), there exist positive integers \(m,n\) of opposite parity for which \(x^m-x^n\in N\cap Z\). We identify some basic properties of such rings and prove some results on commutativity.
16U80 Generalizations of commutativity (associative rings and algebras)
16U70 Center, normalizer (invariant elements) (associative rings and algebras)
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