Rings that are nearly Boolean. II. (English) Zbl 0544.16015
[Part I, cf. ibid. 80, 41-46 (1980; Zbl 0402.16027).]
The author examines the following conjecture: if R is a ring, \(\alpha\) an epimorphism of \(\{R,+\}\) to \(\{R,+\}\) and n a natural number greater than 1, such that \(x^ n-x\alpha \in Z(R)\), the center of R, then R is commutative. The problem is solved for some particular cases.
The author examines the following conjecture: if R is a ring, \(\alpha\) an epimorphism of \(\{R,+\}\) to \(\{R,+\}\) and n a natural number greater than 1, such that \(x^ n-x\alpha \in Z(R)\), the center of R, then R is commutative. The problem is solved for some particular cases.
Reviewer: M.Abad
MSC:
| 16U70 | Center, normalizer (invariant elements) (associative rings and algebras) |
| 06E20 | Ring-theoretic properties of Boolean algebras |
