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On derivations in near-rings. II. (English) Zbl 0911.16026
Saad, Gerhard et al., Nearrings, nearfields and $$K$$-loops. Proceedings of the conference on nearrings and nearfields, Hamburg, Germany, July 30–August 6, 1995. Dordrecht: Kluwer Academic Publishers. Math. Appl., Dordr. 426, 191-197 (1997).
[For part I cf. the author and G. Mason, Near-rings and near-fields, Proc. Conf., Tübingen 1985, North-Holland Math. Stud. 137, 31-35 (1987; Zbl 0619.16024).]
A near-ring $$N$$ with a derivation and such that $$xNy=\{0\}$$ implies that $$x=0$$ or $$y=0$$ and satisfying certain conditions on multiplicative ideals is a commutative ring.
For the entire collection see [Zbl 0874.00036].

##### MSC:
 16Y30 Near-rings 16W25 Derivations, actions of Lie algebras
##### Keywords:
derivations; near-rings; commutativity theorems