On additivity of derivations

G. S. Sandhu, D. Kumar

Abstract


Let $R$ be a ring and $M$ be an $R$-bimodule. A mapping $d:R\rightarrow M$ (not necessarily additive)
is called multiplicative derivation of $R$ if $d(xy)=d(x)y+xd(y)$ for all $x,y\in R.$
In this paper, we intend to establish the additivity of $d$ under some suitable restrictions.
Moreover, we introduce multiplicative semi-derivations of rings and discuss their additivity.

Keywords


derivation, multiplicative derivation, multiplicative semi-derivation, additivity, Peirce decomposition

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