$b$ -Generalized derivations on prime rings

T.  Pehlivan; E. Albaş

doi:10.37863/umzh.v74i6.5989

T. Pehlivan Ege Univ., Izmir, Turkey https://orcid.org/0000-0001-6441-8690
E. Albaş Ege Univ., Izmir, Turkey https://orcid.org/0000-0002-3108-7810

DOI: https://doi.org/10.37863/umzh.v74i6.5989

Keywords: Prime ring, $b$-generalized derivation, homomorphism, anti-homomorphism

Abstract

Let $R$ be a prime ring with center $Z(R)$, right Martindale quotient ring $Q$ and extended centroid $C$. By a $b$-generalized derivation we mean an additive mapping $g:R\rightarrow Q$ such that $g(xy) = g(x)y + bxd(y)$ for all $x,y \in R$, where $b \in Q$ and $d: R \rightarrow Q$ is an additive map. In this paper, we extend some well-known results concerning (generalized) derivations on prime rings to $b$-generalized derivations. Further we investigate $b$-generalized derivation acting as a homomorphism or anti-homomorphism in a prime ring.

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