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arXiv · 2007.08013

There are no nontrivial two-sided multiplicative (generalized)-skew derivations in prime rings

Jose Brox
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Abstract

As originally defined by Ashraf and Mozumder, multiplicative (generalized)-skew derivations must satisfy two identities. In this short note we show that, as a consequence of the simultaneous satisfaction of both identities, a multiplicative (generalized)-skew derivation of a prime ring is either a multiplicative (generalized) derivation (i.e., not skew), or a generalized skew derivation (i.e., additive). Therefore only one of the identities should be taken in the definition of multiplicative (generalized)-skew derivations in order to get a new class of derivations in prime rings.

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Jose Brox. 2020-07-15. There are no nontrivial two-sided multiplicative (generalized)-skew derivations in prime rings. https://arxiv.org/abs/2007.08013

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