• 제목/요약/키워드: generalized ${\ast}$-derivation

검색결과 3건 처리시간 0.016초

Generalized Derivations on ∗-prime Rings

  • Ashraf, Mohammad;Jamal, Malik Rashid
    • Kyungpook Mathematical Journal
    • /
    • 제58권3호
    • /
    • pp.481-488
    • /
    • 2018
  • Let I be a ${\ast}$-ideal on a 2-torsion free ${\ast}$-prime ring and $F:R{\rightarrow}R$ a generalized derivation with an associated derivation $d:R{\rightarrow}R$. The aim of this paper is to explore the condition under which generalized derivation F becomes a left centralizer i.e., associated derivation d becomes a trivial map (i.e., zero map) on R.

REGULARITY OF GENERALIZED DERIVATIONS IN BCI-ALGEBRAS

  • Muhiuddin, G.
    • 대한수학회논문집
    • /
    • 제31권2호
    • /
    • pp.229-235
    • /
    • 2016
  • In this paper we study the regularity of inside (or outside) (${\theta},{\phi}$)-derivations in BCI-algebras X and prove that let $d_{({\theta},{\phi})}:X{\rightarrow}X$ be an inside (${\theta},{\phi}$)-derivation of X. If there exists a ${\alpha}{\in}X$ such that $d_{({\theta},{\phi})}(x){\ast}{\theta}(a)=0$, then $d_{({\theta},{\phi})}$ is regular for all $x{\in}X$. It is also shown that if X is a BCK-algebra, then every inside (or outside) (${\theta},{\phi}$)-derivation of X is regular. Furthermore the concepts of ${\theta}$-ideal, ${\phi}$-ideal and invariant inside (or outside) (${\theta},{\phi}$)-derivations of X are introduced and their related properties are investigated. Finally we obtain the following result: If $d_{({\theta},{\phi})}:X{\rightarrow}X$ is an outside (${\theta},{\phi}$)-derivation of X, then $d_{({\theta},{\phi})}$ is regular if and only if every ${\theta}$-ideal of X is $d_{({\theta},{\phi})}$-invariant.