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Derivations, products of derivations, and commutativity in near-rings. (English) Zbl 1004.16046

The authors deal mainly with zero-symmetric 3-prime near-rings and derivations on them. They study different types of conditions for derivations that imply, for example, that the supporting group of the near-ring is Abelian or the near-ring is commutative; other types of conditions, involving pair of derivations, force one of them to be zero. The last section presents results on higher derivations.

MSC:

16Y30 Near-rings
16W25 Derivations, actions of Lie algebras
16U70 Center, normalizer (invariant elements) (associative rings and algebras)
16U80 Generalizations of commutativity (associative rings and algebras)
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