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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.
##### MSC:
 16U80 Generalizations of commutativity (associative rings and algebras) 16U70 Center, normalizer (invariant elements) (associative rings and algebras)
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##### References:
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