• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1319-1334
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• 2020

In this paper, we study the basic theory of the category of graded w-Noetherian modules over a graded ring R. Some elementary concepts, such as w-envelope of graded modules, graded w-Noetherian rings and so on, are introduced. It is shown that: (1) A graded domain R is graded w-Noetherian if and only if R^g_𝔪 is a graded Noetherian ring for any gr-maximal w-ideal m of R, and there are only finite numbers of gr-maximal w-ideals including a for any nonzero homogeneous element a. (2) Let R be a strongly graded ring. Then R is a graded w-Noetherian ring if and only if R_e is a w-Noetherian ring. (3) Let R be a graded w-Noetherian domain and let a ∈ R be a homogeneous element. Suppose 𝖕 is a minimal graded prime ideal of (a). Then the graded height of the graded prime ideal 𝖕 is at most 1.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.541-547
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• 2008

Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with $n\;{\geq}\;3$. We denote by $M_n(R)$ the ring of all $n{\times}n$ matrices over R. Let ($J_n(R)$) be the additive subgroup of $M_n(R)$ generated additively by all idempotent matrices. Let ($D=J_n(R)$) or $M_n(R)$. In this paper, by using an additive idem potence-preserving result obtained by Coo (see [4]), I characterize (i) the additive preservers of tripotence from D to $M_m(R)$ when 2 and 3 are units of R; (ii) the additive preservers of inverses (respectively, Drazin inverses, group inverses, {1}-inverses, {2}-inverses, {1, 2}-inverses) from $M_n(R)$ to $M_n(R)$ when 2 and 3 are units of R.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.875-880
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• 1995

Let $S_p(\alpha)$ denote the class of the Spirallike functions of order $\alpha, 0 < $\mid$\alpha$\mid$ < \frac{\pi}{2}$ Let $\Pi_N$ denote the subset of $S_p(\alpha)$ consisting of all products $z\Pi^N_{j=1}(1-u_j z)^{-mt_j}$ where $m = 1 + e^{-2i\alpha},$\mid$u_j$\mid$ = 1, t_j > 0$ for $j = 1, \cdots, N$ and $\sum^{N}_{j=1}{t_j = 1}$. In this paper we prove that extreme points of $S_p(\alpha)$ may be found which lie in $\Pi_N$ for some $N \geq 2$. We are let to conjecture that all exreme points of $S_p(\alpha)$ lie in $\Pi_N$ for somer $N \geq 1$ and that every such function is an extreme point.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.221-227
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• 2002

In this paper we will show that the followings ; (1) Let R be a regular local ring of dimension n. Then $A_{n-2}$(R) = 0. (2) Let R be a regular local ring of dimension n and I be an ideal in R of height 3 such that R/I is a Gorenstein ring. Then [I] = 0 in $A_{n-3}$(R). (3) Let R = V[[ $X_1$, $X_2$, …, $X_{5}$ ]]/(p+ $X_1$$^{t1}$ + $X_2$$^{t2}$ + $X_3$$^{t3}$ + $X_4$$^2$+ $X_{5}$ $^2$/), where p $\neq$2, $t_1$, $t_2$, $t_3$ are arbitrary positive integers and V is a complete discrete valuation ring with (p) = mv. Assume that R/m is algebraically closed. Then all the Chow group for R is 0 except the last Chow group.group.oup.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.347-355
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• 2001

Let ($X, \omega$) be a closed symplectic 4-manifold. Let a finite cyclic group G act semifreely, holomorphically on X as isometries with fixed point set $\Sigma$(may be empty) which is a 2-dimension submanifold. Then there is a smooth structure on the quotient X'=X/G such that the projection $\pi$:X$\rightarrow$X' is a Lipschitz map. Let L$\rightarrow$X be the Spin$^c$ -structure on X pulled back from a Spin$^c$-structure L'$\rightarrow$X' and b_2^$+(X')>1. If the Seiberg-Witten invariant SW(L')$\neq$0 of L' is non-zero and $L=E\bigotimesK^-1\bigotimesE$ then there is a G-invariant pseudo-holomorphic curve u:$C\rightarrowX$,/TEX> such that the image u(C) represents the fundamental class of the Poincare dual $c_1$(E). This is an equivariant version of the Taubes' Theorem.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.233-242
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• 2004

The aim of this note is to study properties of the generalized centroid of the semi-prime gamma rings. Main results are the following theorems: (1) Let M be a semi-prime $\Gamma$-ring and Q a quotient $\Gamma$-ring of M. If W is a non-zero submodule of the right (left) M-module Q, then $W\Gamma$W $\neq 0. Furthermore Q is a semi-prime $\Gamma$-ring. (2) Let M be a semi-prime $\Gamma$-ring and $C_{{Gamma}$ the generalized centroid of M. Then $C_{\Gamma}$ is a regular $\Gamma$-ring. (3) Let M be a semi-prime $\Gamma$-ring and $C_{\gamma}$ the extended centroid of M. If $C_{\gamma}$ is a $\Gamma$-field, then the $\Gamma$-ring M is a prime $\Gamma$-ring.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.683-689
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• 2007

Let $\mathcal{B}$ be a certain Banach space consisting of analytic functions defined on a bounded domain G in the complex plane. Let ${\varphi}$ be an analytic polynomial or a rational function and let $M_{\varphi}$ denote the operator of multiplication by ${\varphi}$. Under certain condition on ${\varphi}$ and G, we characterize the commutant of $M_{\varphi}$ that is the set of all bounded operators T such that $TM_{\varphi}=M_{\varphi}T$. We show that $T=M_{\Psi}$, for some function ${\Psi}$ in $\mathcal{B}$.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1203-1220
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• 2008

Let V be an arbitrary system of weights on an open connected subset G of ${\mathbb{C}}^N(N{\geq}1)$ and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let $HV_b$ (G, E) and $HV_0$ (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings ${\phi}:G{\rightarrow}G$ and operator-valued analytic mappings ${\Psi}:G{\rightarrow}B(E)$ which generate weighted composition operators and invertible weighted composition operators on the spaces $HV_b$ (G, E) and $HV_0$ (G, E) for different systems of weights V on G. Also, we obtained compact weighted composition operators on these spaces for some nice classes of weights.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.689-695
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• 2014

Let M be an N-function satisfies the ${\Delta}_2$-condition and let $O_M$ be the Orlicz space associated with M. Let $C(O_M)$ be the space of all continuous functions defined on the interval [0, T] with values in $O_M$. In this note, we define the analogue of Wiener measure $m^M_{\phi}$ on $C(O_M)$, establish the Wiener integration formulae for the cylinder functions on $C(O_M)$ and give some examples related to our formulae.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.269-278
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• 2008

Let ${\partial}D$ be the boundary of the open unit disk D in the complex plane and $L^p({\partial}D)$ the class of all complex, Lebesgue measurable function f for which $\{\frac{1}{2\pi}{\int}_{-\pi}^{\pi}{\mid}f(\theta){\mid}^pd\theta\}^{1/p}<{\infty}$. Let P be the orthogonal projection from $L^p({\partial}D)$ onto ${\cap}_{n<0}$ ker $a_n$. For $f{\in}L^1({\partial}D)$, ${\hat{f}}(z)=\frac{1}{2\pi}{\int}_{-\pi}^{\pi}P_r(t-\theta)f(\theta)d{\theta}$ is the harmonic extension of f. Let ${\hat{P}}$ be the composition of P with the harmonic extension. In this paper, we will show that if $1, then ${\hat{P}}:L^p({\partial}D){\rightarrow}H^p(D)$ is bounded. In particular, we will show that ${\hat{P}}$ is unbounded on $L^{\infty}({\partial}D)$.