TY  - JOUR
T1  - Relationship Between a Homoderivation and a Semi-Derivation
AU  - Türkmen, Selin
PY  - 2024
DA  - June
Y2  - 2024
DO  - 10.53570/jnt.1467690
JF  - Journal of New Theory
JO  - JNT
PB  - Naim ÇAĞMAN
WT  - DergiPark
SN  - 2149-1402
SP  - 28
EP  - 38
IS  - 47
LA  - en
AB  - 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 $\alpha=\vartheta+1$.
KW  - Ring
KW  - semi-derivation
KW  - homoderivation
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UR  - https://doi.org/10.53570/jnt.1467690
L1  - https://dergipark.org.tr/en/download/article-file/3859438
ER  -