On additivity of derivations

Keywords: derivation, multiplicative derivation, multiplicative semi-derivation, additivity, Peirce decomposition
Published online: 2019-12-31


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.

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How to Cite
Sandhu G., Kumar D. On Additivity of Derivations. Carpathian Math. Publ. 2019, 11 (2), 453-462.