• Korean Journal of Mathematics
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• v.7 no.2
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• pp.167-169
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• 1999

Let R be a Noetherian domain. It is proved that $t$-dimR = 1 if and only if each (proper if R is not a valuation domain) $t$-linked overring D of R is of $t$-dimD = 1 if and only if each integrally closed $t$-linked overring of R is a Krull domain.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.9-16
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• 2000

An A-module M is catenary if for each pair of prime submodules K and L of M with $K{\subset}L$ all saturated chains of prime submodules of M from K to L have a common finite length. We show that when A is a Noetherian domain, then every finitely generated A-module is catenary if and only if A is a Dedekind domain or a field. Moreover, a torsion-free divisible A-module M is catenary if and only if the vector space M over Q(A) (the field of fractions of A) is finite dimensional.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.99-104
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• 1994

Let R be a left Artinian ring with identity 1 and let G be the group of units of R. It is shown that if G is finite, then R is finite. It is also shown that if 2.1 is a unit in R, then G is abelian if and only if R is commutative.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.855-866
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• 1995

We prove that if a nals X is reflexive, then $X = W_X + V_X$. We prove also that if an als X has a finite basis, then $X = W_X + V_X$ if and only if X is reflexive.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.85-90
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• 2022

In this article, we consider the notion of expansiveness on compact metric spaces for symbolically point of view. And we show that a homeomorphism is symbolically countably expansive if and only if it is symbolically measure expansive. Moreover, we prove that a homeomorphism is symbolically N-expansive if and only if it is symbolically measure N-expanding.

• Korean Architects
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• s.590
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• pp.108-113
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• 2018

• Economic and Environmental Geology
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• v.47 no.3
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• pp.227-235
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• 2014

For technology level assessment of KIGAM World Class Laboratories (WCL) candidates, bibliometric and qualitative analysis was conducted on their research papers listed on the SCIE database during 2009-2012. For the six research areas of geoscience and mineral resources, a research excellence indicator was applied using a Modified Rank Normalized Impact Factor (mrnIF), which was introduced by Heo et al. (2008) and Cho (2013). The KIGAM research department in rare metals utilization had the highest score for Impact Factor (IF) per paper in 2012 but the groundwater department or the exploration geophysics department came first based on the position and the mrnIF. Applying the mrnIF, the KIGAM research department in groundwater achieved excellent results in 2009 and 2011 and the urban mine department or exploration geophysics department came first place in other years. In the groundwater area, the percentage of research papers over 80 or 90 mrnIF, using Cho (2013)'s research excellence index, was the highest in 2011. The Cho (2013)'s excellent research indicator, 20%, the ratio of over 90 mrnIF was matched in the urban mining area for the whole research period, 2009-2012, and in the groundwater area for several years except 2010. Qualitative analysis of research papers can show the technology level of research departments. KIGAM World Class Laboratories (WCL) candidates should focus on increasing the quality and the quantity of their research papers.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2004.11a
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• pp.245-251
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• 2004

Determination the optimal containership size is the most important factor for competitiveness if shipping companies. Accordingly, the objective if this research is determining the optimal containership size by service routes. Total shipping cost is calculated at the ground if capital cost, vessel operation costs, voyage costs, port charge and miscellaneous cost for 'Europe-Far East', 'Far East-North America' and 'Europe-Far East-North America' Services. Finally, the optimal containership size was utilized through total shipping cost, slot quantity if containership and average throughput by containership.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.847-865
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• 2017

For a finite or an infinite set X, let $2^X$ be the power set of X. A class of simple graph, called strong Boolean graph, is defined on the vertex set $2^X{\setminus}\{X,{\emptyset}\}$, with M adjacent to N if $M{\cap}N={\emptyset}$. In this paper, we characterize the annihilating-ideal graphs $\mathbb{AG}(R)$ that are blow-ups of strong Boolean graphs, complemented graphs and preatomic graphs respectively. In particular, for a commutative ring R such that AG(R) has a maximum clique S with $3{\leq}{\mid}V(S){\mid}{\leq}{\infty}$, we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a complemented graph, if and only if R is a reduced ring. If assume further that R is decomposable, then we prove that $\mathbb{AG}(R)$ is a blow-up of a strong Boolean graph if and only if it is a blow-up of a pre-atomic graph. We also study the clique number and chromatic number of the graph $\mathbb{AG}(R)$.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.87-98
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• 2014

Let R be a commutative ring with identity and M an R-module. In this paper, we associate a graph to M, say ${\Gamma}(M)$, such that when M = R, ${\Gamma}(M)$ is exactly the classic zero-divisor graph. Many well-known results by D. F. Anderson and P. S. Livingston, in [5], and by D. F. Anderson and S. B. Mulay, in [6], have been generalized for ${\Gamma}(M)$ in the present article. We show that ${\Gamma}(M)$ is connected with $diam({\Gamma}(M)){\leq}3$. We also show that for a reduced module M with $Z(M)^*{\neq}M{\backslash}\{0\}$, $gr({\Gamma}(M))={\infty}$ if and only if ${\Gamma}(M)$ is a star graph. Furthermore, we show that for a finitely generated semisimple R-module M such that its homogeneous components are simple, $x,y{\in}M{\backslash}\{0\}$ are adjacent if and only if $xR{\cap}yR=(0)$. Among other things, it is also observed that ${\Gamma}(M)={\emptyset}$ if and only if M is uniform, ann(M) is a radical ideal, and $Z(M)^*{\neq}M{\backslash}\{0\}$, if and only if ann(M) is prime and $Z(M)^*{\neq}M{\backslash}\{0\}$.