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

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

• 대한수학회보
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• 제38권3호
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• pp.443-447
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• 2001

The main goal of this paper is to show the following: Let d and g be (continuous or discontinuous) linear derivations on a Banach algebra A over a complex field C such that $\alphad^3+dg$ is a linear Jordan derivation for some $\alpha\inC$. Then the product dg maps A into the Jacobson radical of A.

• 대한수학회논문집
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• 제31권1호
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• pp.101-113
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• 2016

In this article, we considered the stability of the following (${\alpha}$, ${\beta}$, ${\gamma}$)-derivation $${\alpha}D[x,y]={\beta}[D(x),y]+{\gamma}[x,D(y)]$$ and homomorphisms associated to the quadratic type functional equation $$f(kx+y)+f(kx+{\sigma}(y))=2kg(x)+2g(y),\;x,y{\in}A$$, where ${\sigma}$ is an involution of the Lie $C^*$-algebra A and k is a fixed positive integer. The Hyers-Ulam stability on unbounded domains is also studied. Applications of the results for the asymptotic behavior of the generalized quadratic functional equation are provided.

• 대한수학회논문집
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• 제31권2호
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• pp.229-235
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• 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.

• 대한수학회지
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• 제52권1호
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• pp.191-207
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• 2015

Let $\mathcal{R}$ be a prime ring of characteristic different from 2, $\mathcal{Q}_r$ be its right Martindale quotient ring and $\mathcal{C}$ be its extended centroid. Suppose that $\mathcal{G}$ is a nonzero generalized skew derivation of $\mathcal{R}$, ${\alpha}$ is the associated automorphism of $\mathcal{G}$, f($x_1$, ${\cdots}$, $x_n$) is a non-central multilinear polynomial over $\mathcal{C}$ with n non-commuting variables and $$\mathcal{S}=\{f(r_1,{\cdots},r_n)\left|r_1,{\cdots},r_n{\in}\mathcal{R}\}$$. If $\mathcal{G}$ acts as a Jordan homomorphism on $\mathcal{S}$, then either $\mathcal{G}(x)=x$ for all $x{\in}\mathcal{R}$, or $\mathcal{G}={\alpha}$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권4호
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• pp.237-246
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• 2014

Let M be a prime ${\Gamma}$-ring and let d be a derivation of M. If there exists a fixed integer n such that $(d(x){\alpha})^nd(x)=0$ for all $x{\in}M$ and ${\alpha}{\in}{\Gamma}$, then we prove that d(x) = 0 for all $x{\in}M$. This result can be extended to semiprime ${\Gamma}$-rings.

• Journal of Applied and Pure Mathematics
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• 제4권1_2호
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• pp.1-7
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• 2022

A mapping T : R → R (not necessarily additive) is called multiplicative left 𝛼-centralizer if T(xy) = T(x)𝛼(y) for all x, y ∈ R. A mapping F : R → R (not necessarily additive) is called multiplicative (generalized)(𝛼, 𝛽)-derivation if there exists a map (neither necessarily additive nor derivation) f : R → R such that F(xy) = F(x)𝛼(y) + 𝛽(x)f(y) for all x, y ∈ R, where 𝛼 and 𝛽 are automorphisms on R. The main purpose of this paper is to study some algebraic identities with multiplicative (generalized) (𝛼, 𝛽)-derivations and multiplicative left 𝛼-centralizer on the left ideal of a prime ring R.

• 대한수학회지
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• 제42권2호
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• pp.353-363
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• 2005

For a ring endomorphism $\alpha$ and an $\alpha$-derivation $\delta$, we introduce ($\alpha$, $\delta$)-skew Armendariz rings which are a generalization of $\alpha$-rigid rings and Armendariz rings, and investigate their properties. A semi prime left Goldie ring is $\alpha$-weak Armendariz if and only if it is $\alpha$-rigid. Moreover, we study on the relationship between the Baerness and p.p. property of a ring R and these of the skew polynomial ring R[x; $\alpha$, $\delta$] in case R is ($\alpha$, $\delta$)-skew Armendariz. As a consequence we obtain a generalization of [11], [14] and [16].

• 한국자원식물학회지
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• 제20권6호
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• pp.548-552
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• 2007

This research is the basic research to develop new anti-inflammatory medicine by feeding Scutellariae Radix extract to lipopolysaccharide(LPS) exposed rats, and analyzed it's effect on inflammatory response by LPS derivation. As a result, Plasma interleukin-$1\beta(IL-1\beta)$ and Plasma interleukin-6(IL-6) concentration showed the highest point at 5h after LPS injection, and in this time, the concentration of $IL-1\beta$ and IL-6 in the Scutellariae Radix extract groups at 200mg/kg and 300mg/kg showed lower values than that of control group. Plasma tumor necrosis $factor-\alpha(TNF-\alpha)$ concentration after LPS injection showed the highest point at 2h and showed similar level till at 5h. $TNF-\alpha$ concentration at 2h after LPS injection showed the low value only in the Scutellariae Radix extract 300mg/kg group compared to others, and in 5h, the all Scutellariae Radix extract groups showed lower value than that of the control group. Plasma interleukin-10(IL-10) concentration increased at 2h after LPS injection and reached the highest at 5h. After LPS injection the IL-10 concentration at 2h, the Scutellariae Radix extract injection group at 300mg/kg showed higher value than that of the others, and in 5h after LPS injection, Scutellariae Radix extract 200mg and 300mg groups showed higher value than the control group. Concluding from the above results, in inflammatory response by LPS derivation, the Scutellariae Radix gives positive effect.

• 대한수학회논문집
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• 제27권1호
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• pp.69-76
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• 2012

Let R be a ring, and ${\alpha}$ be an endomorphism of R. An additive mapping H : R ${\rightarrow}$ R is called a left ${\alpha}$-multiplier (centralizer) if H(xy) = H(x)${\alpha}$(y) holds for all x,y $\in$ R. In this paper, we shall investigate the commutativity of prime and semiprime rings admitting left ${\alpha}$-multiplier satisfying any one of the properties: (i) H([x,y])-[x,y] = 0, (ii) H([x,y])+[x,y] = 0, (iii) $H(x{\circ}y)-x{\circ}y=0$, (iv) $H(x{\circ}y)+x{\circ}y=0$, (v) H(xy) = xy, (vi) H(xy) = yx, (vii) $H(x^2)=x^2$, (viii) $H(x^2)=-x^2$ for all x, y in some appropriate subset of R.