• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1205-1215
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• 2018

In this paper, a boundary version of the $Carath{\acute{e}}odory^{\prime}s$ inequality is investigated. We shall give an estimate below ${\mid}f^{\prime}(b){\mid}$ according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and $z_1{\neq}0$. The sharpness of these estimates is also proved.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.653-659
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• 2009

It is proved that if $M\;=\;B_p(3)$ or $C_p(3)$, p is an odd prime, G is a finite group and has the same order components of M, then $G\;{\cong}\;Bp(3)$ or $C_p(3)$.

• Kyungpook Mathematical Journal
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• v.18 no.1
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• pp.105-107
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• 1978

Considering the prime z-filters on a topological space X through the structures of the ring C(X) of continuous functions. a prime z-filter is uniquely determined by a primary z-ideal in the ring C(X), i. e., they have a one-to-one correspondence. Any primary ideal is contained in a unique maximal ideal in C(X). Denoting $\mathfrak{F}(X)$, $\mathfrak{Q}(X)$, 𝔐(X) the prime, primary-z, maximal spectra, respectively, $\mathfrak{Q}(X)$ is neither an open nor a closed subspace of $\mathfrak{F}(X)$.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.21-28
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• 2015

Let R be a prime ring with center Z, I a nonzero ideal of R, and ${\sigma}$ a non-trivial automorphism of R such that $\{(x{\circ}y)^{\sigma}-(x{\circ}y)\}^n{\in}Z$ for all $x,y{\in}I$. If either char(R) > n or char (R) = 0, then R satisfies $s_4$, the standard identity in 4 variables.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.41-50
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• 2015

The purpose of this paper is to prove some results which are of independent interest and related to additive maps on ${\sigma}$-prime rings. Further, examples are given to demonstrate that the restrictions imposed on the hypotheses of these results are not superfluous.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.351-366
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• 2007

Let R be a commutative ring and let M be an R-module. Let X = Spec(M) be the prime spectrum of M with Zariski topology. Our main purpose in this paper is to specify the topological dimensions of X, where X is a Noetherian topological space, and compare them with those of topological dimensions of $Supp_{R}$(M). Also we will give a characterization for the irreducibility of X and we obtain some related results.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.481-488
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• 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.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.21-30
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• 2000

Lipschitz Algebras Lip(X, ${\alpha}$) and lip(X, ${\alpha}$) were first studied by D. R. Sherbert in 1964. B. Pavlovic in 1995 shown that in these algebras, the prime ideals containing a given prime ideal form a chain. In this paper, we show that the above property holds in $Lip^n(X,\;{\alpha})$ and $lip^n(X,\;{\alpha})$, the Lipschitz algebras of finite differentiable functions on a perfect compact place set X.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.101-106
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• 2006

Let R be a prime ring and I a nonzero ideal of R. Let $\alpha,\;\nu,\;\tau\;R{\rightarrow}R$ be the endomorphisms and $\beta,\;\mu\;R{\rightarrow}R$ the automorphisms. If R admits a generalized $(\alpha,\;\beta)-derivation$ g associated with a nonzero $(\alpha,\;\beta)-derivation\;\delta$ such that $g([\mu(x),y])\;=\;[\nu/(x),y]\alpha,\;\tau$ for all x, y ${\in}I$, then R is commutative.

• Bulletin of the Korean Chemical Society
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• v.22 no.9
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• pp.975-978
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• 2001

A novel poly[9,10-diphenylanthracene-4',4"-ylenevinylene-3,6-(N-2-ethyl hexyl)carbazole] containing alternate diphenylanthracene and carbazole unit was synthesized by the Wittig reaction. The obtained polymer was soluble in common organic solvents and thermally stable up to 380 $^{\circ}C.$ The polymer gives rise to bright blue fluorescence both in solution and in thin solid films. The light emitted from the device (ITO/polymer/Al) was greenish-blue in color and clearly visible in daylight.