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Nonexistence of nonzero derivations on some classes of zero-symmetric 3-prime near-rings

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We give some classes of zero-symmetric 3-prime near-rings such that every member of these classes has no nonzero derivation. Moreover, we extend the concept of “3-prime” to subsets of near-rings and use it to generalize Theorem 1.1 due to Fong, Ke, and Wang concerning the transformation near-rings M o (G) by using a different technique and a simpler proof.

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Correspondence to A. A. M. Kamal.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 3, pp. 420–424, March, 2014.

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Kamal, A.A.M., Al-Shaalan, K.H. Nonexistence of nonzero derivations on some classes of zero-symmetric 3-prime near-rings. Ukr Math J 66, 473–478 (2014). https://doi.org/10.1007/s11253-014-0945-4

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