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On generalized semiderivations of \(\Gamma\)-rings. (English) Zbl 1370.16044

Summary: In this paper, we introduce the notion of a generalized semiderivation on \(\Gamma\)-ring, and we try to generalize some known results of derivations, semiderivations and generalized derivations to generalized semiderivations on a prime \(\Gamma\)-ring. We also prove that there exist no nontrivial generalized semiderivations which act as a homomorphism or as an antihomomorphism on a prime \(\Gamma\)-ring.

MSC:

16Y99 Generalizations
16W25 Derivations, actions of Lie algebras
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