English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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 (generalized)-$(\alpha,\beta)$-derivation associated with $d$ if $F(xy)-F(x)\alpha(y)-\beta(x)d(y)\in Z$ for all $x, y \in R$. The objective of the present paper is to study the following conditions: (i) $F(xy)\pm \beta(x)G(y)\in Z$, (ii) $F(xy)\pm g(x)\alpha(y)\in Z$ and (iii) $F(xy)\pm g(y)\alpha(x)\in Z$ for all $x,y$ in some appropriate subsets of $R$, where $G$ is a multiplicative $($generalized$)$-$(\alpha,\beta)$-derivation of $R$ associated with the map $g$ on $R$.

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