• 대한수학회논문집
• /
• 제8권4호
• /
• pp.555-560
• /
• 1993

• East Asian mathematical journal
• /
• 제3권
• /
• pp.13-19
• /
• 1987

• Kyungpook Mathematical Journal
• /
• 제29권1호
• /
• pp.5-6
• /
• 1989

• Kyungpook Mathematical Journal
• /
• 제30권1호
• /
• pp.75-79
• /
• 1990

• 충청수학회지
• /
• 제33권3호
• /
• pp.307-318
• /
• 2020

In this paper, we extend the notion of a generalized derivation F associated with derivation d to two generalized derivations F and G associated with the same derivation d, as a new idea, to obtain the commutativity of prime rings under certain conditions.

• 대한수학회논문집
• /
• 제33권1호
• /
• pp.103-125
• /
• 2018

Let R be a 5!-torsion free semiprime ring, and let $D:R{\rightarrow}R$ be a Jordan derivation on a semiprime ring R. Then $[D(x),x]D(x)^2=0$ if and only if $D(x)^2[D(x), x]=0$ for every $x{\in}R$. In particular, let A be a Banach algebra with rad(A) and if D is a continuous linear Jordan derivation on A, then we show that $[D(x),x]D(x)2{\in}rad(A)$ if and only if $D(x)^2[D(x),x]{\in}rad(A)$ for all $x{\in}A$ where rad(A) is the Jacobson radical of A.

• Korean Journal of Mathematics
• /
• 제28권3호
• /
• pp.603-611
• /
• 2020

In this manuscript, we discuss the relationship between prime rings and automorphisms satisfying differential identities involving commutators and anti-commutators on Lie ideals. In addition, we provide an example which shows that we cannot expect the same conclusion in case of semiprime rings.

• 대한수학회논문집
• /
• 제23권4호
• /
• pp.469-477
• /
• 2008

We introduce the notion of two-sided $\Gamma$-$\alpha$-derivation of a $\Gamma$-near-ring and give some generalizations of [1, 2].

• 대한수학회논문집
• /
• 제17권4호
• /
• pp.607-618
• /
• 2002

Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A \longrightarrowA such that D($\chi$)[D($\chi$),$\chi$]D($\chi$) $\in$ rad(A) for all $\chi$ A. In this case, we have D(A) ⊆ rad(A).

• 대한수학회보
• /
• 제42권4호
• /
• pp.671-678
• /
• 2005

Let R be a noncommutative semi prime ring. Suppose that there exists a derivation d : R $\to$ R such that for all x $\in$ R, either [[d(x),x], d(x)] = 0 or $\langle$$\langle(x),\;x\rangle,\;d(x)\rangle$ = 0. In this case [d(x), x] is nilpotent for all x $\in$ R. We also apply the above results to a Banach algebra theory.