Remarks on the notion of homo-derivations

Gselmann, Eszter and Kiss, Gergely (2020) Remarks on the notion of homo-derivations. ANNALES UNIVERSITATIS SCIENTIARUM BUDAPESTINENSIS DE ROLANDO EOTVOS NOMINATAE SECTIO COMPUTATORICA. ISSN 0138-9491

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Abstract

The purpose of this paper is to study the (different) notions of homo-derivations. These are additive mappings f of a ring R that also fulfill the identity f(xy)=f(x)y+xf(y)+f(x)f(y)(x,y∈R), or (in case of the other notion) the system of equations f(xy)=f(x)f(y) f(xy)=f(x)y+xf(y)(x,y∈R). Our primary aim is to investigate the above equations without additivity as well as the following Pexiderized equation f(xy)=h(x)h(y)+xk(y)+k(x)y. The obtained results show that under rather mild assumptions homo-derivations can be fully characterized, even without the additivity assumption.

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