• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권3호
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• pp.181-191
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• 2018

In the present paper, we investigate the action of generalized derivation G associated with a derivation g in a (semi-) prime ring R satisfying $(G([x,y])-[G(x),y])^n=0$ for all x, $y{\in}I$, a nonzero ideal of R, where n is a fixed positive integer. Moreover, we also examine the above identity in Banach algebras.

• 대한수학회논문집
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• 제17권4호
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• pp.607-618
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• 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
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• 제39권2호
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• pp.211-224
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• 2002

In this paper we show that if D is a continuous linear Jordan derivation on a Banach algebra A satisfying [[D($x^{n}$), $x^{n}$, $x^{n}$] $\in$ rad(A) for a positive integer n and for all x${\in}$A, then D maps A into rad(A).

• Korean Journal of Mathematics
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• 제24권4호
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• pp.587-600
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• 2016

We obtain the general solution of the functional equation $f(ax+y)-f(x-ay)+{\frac{1}{2}}a(a^2+1)f(x-y)+(a^4-1)f(y)={\frac{1}{2}}a(a^2+1)f(x+y)+(a^4-1)f(x)$ and prove the stability problem of the quartic Lie ${\ast}$-derivation by using a directed method and an alternative fixed point method.

• 한국콘텐츠학회:학술대회논문집
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• 한국콘텐츠학회 2003년도 추계종합학술대회 논문집
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• pp.245-248
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• 2003

본 논문은 미분가군이 가환대수에서 정의된 미분가군과 임의의 다원환에 대하여 정의된 Bergman 의 관점에서 본 미분가군으로서 보편적 미분가군과 다른 구조를 갖는 미분가군 동형사상에 의하여 유일하게 결정될 수 있다는 것을 밝히는 것이다.

• Korean Journal of Mathematics
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• 제19권1호
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• pp.87-99
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• 2011

Using the Hyers-Ulam-Rassias stability method of functional equations, we investigate homomorphisms in proper $CQ^*$-algebras and proper Lie $CQ^*$-algebras, and derivations on proper $CQ^*$-algebras and proper Lie $CQ^*$-algebras associated with the following functional equation $$\frac{1}{k}f(kx+ky+kz)=f(x)+f(y)+f(z)$$ for a fixed positive integer $k$.

• Korean Journal of Mathematics
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• 제25권2호
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• pp.163-179
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• 2017

In this paper, we introduce the notion of left derivations of BCH algebras and investigate some properties of left derivations in a BCH-algebra. Moreover, we introduce the notions of fixed set and kernel set of derivations in a BCH-algebra and obtained some interesting properties in medial BCH-algebras. Also, we discuss the relations between ideals in a medial BCH-algebras.

• 대한수학회보
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• 제42권4호
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• pp.671-678
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• 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.

• 대한수학회논문집
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• 제12권2호
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• pp.251-256
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• 1997

We show that a strong system of derivations ${D_0, D_1,\cdots,D_m}$ on a commutative Banach algebra A is contained in the radical of A if it satisfies one of the following conditions for separating spaces; (1) $\partial(D_i) \subseteq rad(A) and \partial(D_i) \subseteq K D_i(rad(A))$ for all i, where $K D_i(rad(A)) = {x \in rad(A))$ : for each $m \geq 1, D^m_i(x) \in rad(A)}$. (2) $(D^m_i) \subseteq rad(A)$ for all i and m. (3) $\bar{x\partial(D_i)} = \partial(D_i)$ for all i and all nonzero x in rad(A).

• 대한수학회논문집
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• 제31권2호
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• pp.209-216
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• 2016

In this paper, we introduce the notion of symmetric bi-derivations of a B-algebra and investigate some related properties. We study the notion of symmetric bi-derivations of a 0-commutative B-algebra and state some related properties.