• 충청수학회지
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• 제22권3호
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• pp.451-458
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• 2009

Let $n{\geq}2$ be a fixed positive integer and let R be a noncommutative n!-torsion free semiprime ring. Suppose that there exists a symmetric n-derivation $\Delta$ : $R^{n}{\rightarrow}R$ such that the trace of $\Delta$ is centralizing on R. Then the trace is commuting on R. If R is a n!-torsion free prime ring and $\Delta{\neq}0$ under the same condition. Then R is commutative.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권2호
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• pp.127-138
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• 2015

The object of this paper is to emphasize the role of 'common limit range property' and utilize the same with variants of R-weakly commuting mappings for the existence of common fixed point under strict contractive conditions in metric spaces. We also furnish some interesting examples to validate our main result. Our results improve a host of previously known results including the ones contained in Pant [Contractive conditions and common fixed points, Acta Math. Acad. Paedagog. Nyhàzi. (N.S.) 24(2) (2008), 257-266 MR2461637 (2009h:54061)]. In the process, we also derive a fixed point result satisfying $\phi$-contractive condition.

• 대한수학회보
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• 제51권1호
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• pp.207-211
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• 2014

The aim of this paper is to prove the next result. Let n > 1 be an integer and let R be a n!-torsion free semiprime ring. Suppose that f : R ${\rightarrow}$ R is an additive mapping satisfying the relation [f(x), $x^n$] = 0 for all $x{\in}R$. Then f is commuting on R.

• Kyungpook Mathematical Journal
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• 제48권3호
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• pp.433-442
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• 2008

In this paper we consider a real hypersurface M in complex hyperbolic space $H_n\mathbb{C}$ satisfying $S{\phi}A\;=\;{\phi}AS$, where $\phi$, A and S denote the structure tensor, the shape operator and the Ricci tensor of M respectively. Moreover, we give a characterization of real hypersurfaces of type A in $H_n\mathbb{C}$ by such a commuting Ricci tensor.

• 대한수학회논문집
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• 제28권4호
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• pp.643-647
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• 2013

Let G be a group and let $p$ be a prime number. If the set $\mathcal{A}(G)$ of all commuting automorphisms of G forms a subgroup of Aut(G), then G is called $\mathcal{A}(G)$-group. In this paper we show that any $p$-group with cyclic maximal subgroup is an $\mathcal{A}(G)$-group. We also find the structure of the group $\mathcal{A}(G)$ and we show that $\mathcal{A}(G)=Aut_c(G)$. Moreover, we prove that for any prime $p$ and all integers $n{\geq}3$, there exists a non-abelian $\mathcal{A}(G)$-group of order $p^n$ in which $\mathcal{A}(G)=Aut_c(G)$. If $p$ > 2, then $\mathcal{A}(G)={\cong}\mathbb{Z}_p{\times}\mathbb{Z}_{p^{n-2}}$ and if $p=2$, then $\mathcal{A}(G)={\cong}\mathbb{Z}_2{\times}\mathbb{Z}_2{\times}\mathbb{Z}_{2^{n-3}}$ or $\mathbb{Z}_2{\times}\mathbb{Z}_2$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권4호
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• pp.287-292
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• 2004

The operator $A \; {\in} \; L(H_{i})$, the Banach algebra of bounded linear operators on the complex infinite dimensional Hilbert space $\cal H_{i}$, is said to be p-hyponormal if $(A^\ast A)^P \geq (AA^\ast)^p$ for $p\; \in \; (0,1]$. Let (equation omitted) denote the completion of (equation omitted) with respect to some crossnorm. Let $I_{i}$ be the identity operator on $H_{i}$. Letting (equation omitted), where each $A_{i}$ is p-hyponormal, it is proved that the commuting n-tuple T = ($T_1$,..., $T_{n}$) satisfies Bishop's condition ($\beta$) and that if T is Weyl then there exists a non-singular commuting n-tuple S such that T = S + F for some n-tuple F of compact operators.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권4호
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• pp.271-278
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• 2007

Let R be a 2-torsion free semiprime ring. Suppose that there exists a 4-permuting 4-derivation ${\Delta}:R{\times}R{\times}R{\times}R{\rightarrow}R$ such that the trace is centralizing on R. Then the trace of ${\Delta}$ is commuting on R. In particular, if R is a 3!-torsion free prime ring and ${\Delta}$ is nonzero under the same condition, then R is commutative.

• 대한수학회보
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• 제39권4호
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• pp.635-643
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• 2002

Our main goal is to show that if there exist Jordan derivations D and G on a noncommutative (n + 1)!-torsion free prime ring R such that $$D(x)x^n-x^nG(x)\in\ C(R)$$ for all $x\in\ R$, then we have D=0 and G=0. We also prove that if there exists a derivation D on a noncommutative 2-torsion free prime ring R such that the mapping $\chi$longrightarrow[aD($\chi$), $\chi$] is commuting on R, then we have either a = 0 or D = 0.

• East Asian mathematical journal
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• 제7권1호
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• pp.61-70
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• 1991

• 대한수학회보
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• 제50권1호
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• pp.117-123
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• 2013

Let G be a finite non-abelian group. We define the non-commuting graph ${\nabla}(G)$ of G as follows: the vertex set of ${\nabla}(G)$ is G-Z(G) and two vertices x and y are adjacent if and only if $xy{\neq}yx$. In this paper we prove that if G is a finite group with $${\nabla}(G){\simeq_-}{\nabla}(\mathbb{A}_{22})$$, then $$G{\simeq_-}\mathbb{A}_{22}$$where $\mathbb{A}_{22}$ is the alternating group of degree 22.