On additivity of derivations

G.S. Sandhu; D. Kumar

doi:10.15330/cmp.11.2.453-462

G.S. Sandhu Patel Memorial National College Rajpura, 140401, Punjab, India https://orcid.org/0000-0001-8618-6325
D. Kumar Punjabi University, 147002, Patiala, India

https://doi.org/10.15330/cmp.11.2.453-462

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

Published online: 2019-12-31

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.