On centrally-extended multiplicative (generalized)-$(\alpha,\beta)$-derivations in semiprime rings

Authors : Najat MUTHANA, Zakeiah ALKHAMİSİ

Pages : 578-585

Doi:10.15672/hujms.568378

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Publication Date : 2020-04-02

Article Type : Research Paper

Abstract :Let $R$ be a ring with center $Z$ and $\alpha$, $\beta$ and $d$ mappings of $R$. A mapping $F$ of $R$ is called a centrally-extended multiplicative insert ignore into journalissuearticles values(generalized);-$insert ignore into journalissuearticles values(\alpha,\beta);$-derivation associated with $d$ if $Finsert ignore into journalissuearticles values(xy);-Finsert ignore into journalissuearticles values(x);\alphainsert ignore into journalissuearticles values(y);-\betainsert ignore into journalissuearticles values(x);dinsert ignore into journalissuearticles values(y);\in Z$ for all $x, y \in R$. The objective of the present paper is to study the following conditions: insert ignore into journalissuearticles values(i); $Finsert ignore into journalissuearticles values(xy);\pm \betainsert ignore into journalissuearticles values(x);Ginsert ignore into journalissuearticles values(y);\in Z$, insert ignore into journalissuearticles values(ii); $Finsert ignore into journalissuearticles values(xy);\pm ginsert ignore into journalissuearticles values(x);\alphainsert ignore into journalissuearticles values(y);\in Z$ and insert ignore into journalissuearticles values(iii); $Finsert ignore into journalissuearticles values(xy);\pm ginsert ignore into journalissuearticles values(y);\alphainsert ignore into journalissuearticles values(x);\in Z$ for all $x,y$ in some appropriate subsets of $R$, where $G$ is a multiplicative $insert ignore into journalissuearticles values($generalized$);$-$insert ignore into journalissuearticles values(\alpha,\beta);$-derivation of $R$ associated with the map $g$ on $R$.
Keywords : Semiprime ring, left ideal, multiplicative generalized, derivation, multiplicative generalized, alpha, eta, deri