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A note on a theorem of Jacobson related to periodic rings
Journal article   Open access  Peer reviewed

A note on a theorem of Jacobson related to periodic rings

D.D. Anderson and P.V. Danchev
Proceedings of the American Mathematical Society, Vol.148, pp. 5087-5089
2020
DOI: 10.1090/proc/15246
url
https://doi.org/10.1090/proc/15246View
Published (Version of record) Open Access

Abstract

We show that if R is a ring such that for each x ∈ R there exist two natural numbers n(x) and m(x) of opposite parity with xn(x) = xm(x), then R is commutative. This extends the classical famous theorem of Jacobson [Ann. of Math. 46 (1945), p. 695–707] for commutativity of potent rings. © 2020 American Mathematical Society
Commutativity Jacobson radical Jacobson theorem Periodic rings

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