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DOI: 10.46698/q036935942531z A Note on Periodic Rings
Danchev, P. V.
Vladikavkaz Mathematical Journal 2021. Vol. 23. Issue 4.
Abstract:
We obtain a new and nontrivial characterization of periodic rings (that are those rings \(R\) for which, for each element \(x\) in \(R\), there exists two different integers \(m\), \(n\) strictly greater than \(1\) with the property \(x^m=x^n\)) in terms of nilpotent elements which supplies recent results in this subject by CuiDanchev published in (J. Algebra & Appl., 2020) and by AbyzovTapkin published in (J. Algebra & Appl., 2022). Concretely, we state and prove the slightly surprising fact that an arbitrary ring \(R\) is periodic if, and only if, for every element \(x\) from \(R\), there are integers \(m>1\) and \(n>1\) with \(m\not= n\) such that the difference \(x^mx^n\) is a nilpotent.
Keywords: potent rings, periodic rings, nilpotent elements
Language: English
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For citation: Danchev, P. V. A Note on Periodic Rings, Vladikavkaz Math. J., 2021, vol. 23, no. 4, pp.109111. DOI 10.46698/q036935942531z ← Contents of issue 
 

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