• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.187-191
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• 1996

Let C be a nonsingular complex projective algebraic curve (or a compact Riemann surface) of genus g. Let $M(C)$ denote the field of meromorphic functions on C and N the set of all non-negative integers.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.319-326
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• 2004

In this article, we investigate invertible interpolation problems in Alg(equation omitted) : Let(equation omitted) be a subspace lattice on a Hilbert space H and let X and Y be operators acting on H. When does there exist an invertible operator A in Alg(equation omitted) such that AX = Y?

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.43-50
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• 2017

Let A(n) denote the largest absolute value of the coefficients of n-th cyclotomic polynomial ${\Phi}_n(x)$ and let p < q < r be odd primes. In this note, we give an infinite family of cyclotomic polynomials ${\Phi}_{pqr}(x)$ with A(pqr) = 3, without fixing p.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.65-76
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• 2006

Let $\tau$ be a hereditary torsion theory and let p be a prime ideal of a commutative ring R. We study the existence of (minimal) $\tau-injective$ submodules of the injective hull of R/p.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.525-527
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• 2019

Let X be a completely regular space and let β(X) be the Stone-Čech compactification of X. A flow 𝜙 on X can be extended to a flow 𝚽 on β(X).

• The Mathematical Education
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• v.22 no.1
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• pp.21-23
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• 1983

(1) Let f : XlongrightarrowX' be a homomorphism of BCK-algebras and let A,B be ideals of X and X' respectively such that f(A)⊂B. Then there is a unique homomorphism h : X/AlongrightarrowX'/B such that the diagram(equation omitted) commutes. (2) The class of all complexes of BCK-algebras becomes a category.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.509-520
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• 2003

Let p be a prime number, $Q_{p}$ the field of p-adic numbers, K a finite extension of $Q_{p}$, $\bar{K}}$ a fixed algebraic closure of K and $C_{p}$ the completion of K with respect to the p-adic valuation. Let E be a closed subfield of $C_{p}$, containing K. Given elements $t_1$...,$t_{r}$ $\in$ E for which the field K($t_1$...,$t_{r}$) is dense in E, we construct integral bases of E over K.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.735-740
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• 2001

Let K be a convex body of constant relative breadth and let $K^*$ be its polar dual with respect to the Euclidean unit circle. In this paper we obtain the lower bound for the volume of the pedal body $PK^*P $K^{*}$ of K^*.$ Using this, we also obtain the lower bound for the volume product V$(PK^*)$V(PK) for planar bodies.s.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.409-422
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• 2012

Let $\mathcal{L}$ be a subspace lattice on a Hilbert space $\mathcal{H}$. And let X and Y be operators acting on a Hilbert space $\mathcal{H}$. Let $sp(x)=\{{\alpha}x\;:\;{\alpha}{\in}\mathcal{C}\}$ $x{\in}\mathcal{H}$. Assume that $\mathcal{H}=\overline{range\;X}{\oplus}sp(h)$ for some $h{\in}\mathcal{H}$ and < $h$, $E^{\bot}Xf$ >= 0 for each $f{\in}\mathcal{H}$ and $E{\in}\mathcal{L}$. Then there exists an operator A in Alg$\mathcal{L}$ such that AX = Y if and only if $sup\{\frac{{\parallel}E^{\bot}Yf{\parallel}}{{\parallel}E^{\bot}Yf{\parallel}}\;:\;f{\in}H,\;E{\in}\mathcal{L}\}$ = K < ${\infty}$. Moreover, if the necessary condition holds, then we may choose an operator A such that AX = Y and ${\parallel}||A{\parallel}=K$.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.59-66
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• 2008

Keskin and Harmanci defined the family B(M,X) = ${A{\leq}M|{\exists}Y{\leq}X,{\exists}f{\in}Hom_R(M,X/Y),\;Ker\;f/A{\ll}M/A}$. And Orhan and Keskin generalized projective modules via the class B(M, X). In this note we introduce X-local summands and X-hollow modules via the class B(M, X). Let R be a right perfect ring and let M be an X-lifting module. We prove that if every co-closed submodule of any projective module P contains Rad(P), then M has an indecomposable decomposition. This result is a generalization of Kuratomi and Chang's result [9, Theorem 3.4]. Let X be an R-module. We also prove that for an X-hollow module H such that every non-zero direct summand K of H with $K{\in}B$(H, X), if $H{\oplus}H$ has the internal exchange property, then H has a local endomorphism ring.