Abstract
Let R be a ring such that \(R=R_1+R_2\), where \(R_1\) is a PI subring of R and \(R_2\) is an additive subgroup of R which satisfies a polynomial identity. We prove that if for some integer \(n\ge 1\) either \((R_1R_2)^n \subseteq R_1\) or \((R_2R_1)^n \subseteq R_1\), then R is a PI ring.
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Acknowledgements
The research of Marek Kȩpczyk was supported by Bialystok University of Technology Grant S/WI/1/2016.
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Kȩpczyk, M. Note on rings which are sums of a subring and an additive subgroup. AAECC 32, 359–364 (2021). https://doi.org/10.1007/s00200-020-00479-z
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DOI: https://doi.org/10.1007/s00200-020-00479-z