Relationship Between a Homoderivation and a Semi-Derivation

Authors : Selin Türkmen

Pages : 28-38

Doi:10.53570/jnt.1467690

View : 103 | Download : 110

Publication Date : 2024-06-30

Article Type : Research Paper

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 $\\alpha=\\vartheta+1$.
Keywords : Ring, semi derivation, homoderivation