@article{article_1467690, title={Relationship Between a Homoderivation and a Semi-Derivation}, journal={Journal of New Theory}, pages={28–38}, year={2024}, DOI={10.53570/jnt.1467690}, author={Türkmen, Selin}, keywords={Ring, semi-derivation, homoderivation}, abstract={Let $\wp$ be a ring. It is shown that if an additive mapping $\vartheta$ is a zero-power valued on $\wp$, then $\alpha:\wp\rightarrow\wp$ such that $\alpha=\vartheta+1$ is a bijective mapping of $\wp.$ The main aim of this study is to prove that $\vartheta$ is a homoderivation of $\wp$ if and only if $\vartheta:\wp\rightarrow\wp$ such that $\vartheta=\alpha-1$ is a semi-derivation associated with $\alpha$, where $\alpha:\wp\rightarrow\wp$ is a homomorphism of $\wp.$ Moreover, if $\vartheta$ is a zero-power valued homoderivation on $\wp,$ then $\vartheta$ is a semi-derivation associated with $\alpha$, where $\alpha :\wp\rightarrow\wp$ is an automorphism of $\wp$ such that $\alpha=\vartheta+1$.}, number={47}, publisher={Naim ÇAĞMAN}