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Rings that are nearly Boolean. III. (English) Zbl 0604.16028

[Part II, cf. ibid. 83, 165-167 (1983; Zbl 0544.16015.]
The author studies the following conjecture, a generalization of a theorem of Herstein: If R is a ring such that \(x^ n-\alpha (x)\) is central for all \(x\in R\), where n is a fixed integer \(>1\) and \(\alpha\) is an additive homomorphism of R onto R, then R is commutative. The conjecture is verified in the case \(n=2^ i+2^ j\), \(i>j>0\), and R has unity.
Reviewer: M.Abad

MSC:

16U70 Center, normalizer (invariant elements) (associative rings and algebras)
06E20 Ring-theoretic properties of Boolean algebras
16U99 Conditions on elements
16E50 von Neumann regular rings and generalizations (associative algebraic aspects)

Citations:

Zbl 0544.16015
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