• 충청수학회지
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• 제29권1호
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• pp.137-150
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• 2016

We introduce a new approach that allows us to solve, algorithmically, the contractive completion problem. In this article, we provide concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size $4{\times}4$ using a Moore-Penrose inverse of a matrix.

• 충청수학회지
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• 제25권1호
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• pp.105-113
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• 2012

Generalizing modular lattices, a concept of modular ordered sets was introduced by Chajda and Rachunek. In this paper, we characterize modular ordered sets as those partially ordered set P satisfying that for $a,\;b,\;c\;{\in}\;P\;with\;b\;{\leq}\;c,\;l(a,\;b)\;=\;l(a,\;c)\;and\;u(a,\;b)\;=\;u(a,\;c)$ imply $b\;=\;c$. Using this, we obtain a sufficient condition for them. We also discuss the modularity of the Dedekind-MacNeille completions of ordered sets.

• Kyungpook Mathematical Journal
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• 제14권1호
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• pp.113-117
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• 1974

• East Asian mathematical journal
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• 제14권1호
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• pp.141-148
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• 1998

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제5권
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• pp.473-484
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• 1997

• 대한수학회논문집
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• 제17권4호
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• pp.681-691
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• 2002

We study categorical properties of the category SWQOS (S$\^$U/WQOS, S$\^$L/WQOS, resp) of (upper, lower, resp.) semi-continuous quasi-ordered spaces and the subcategory SWPOS (S$\^$U/WPOS, S$\^$L/WPOS, resp.) of (upper, lower, resp.) semicontinuous partially ordered spaces. We show that the categories S$\^$U/WPOS, S$\^$L/WPOS and SWPOS are closed under the formation of initial mono-sources in the category TQOS of topological quasi-ordered spaces, and they we mono-topological, complete and cocomplete epireflective subcategories of the category TQOS. We obtain their MacNeille and universal initial completions, as well as those of subcatego.ies S$\^$U/WQOS(S$\^$L/WQOS) and SWQOS, in which the topologies are T$\_$0/ and T$_1$, respectively.

• 대한수학회지
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• 제42권2호
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• pp.291-304
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• 2005

We introduce a concept of Cauchy complete Csaszar frames and construct Cauchy completions of Csaszar frames using strict extensions of frames and show that the Cauchy completion gives rise to a coreflection in the categories CsFrm and UCsFrm.

• 충청수학회지
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• 제24권3호
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• pp.587-593
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• 2011

We find concrete necessary and sufficient conditions for the existence of contractive completions of Stochastic Hankel partial contractions of size $4{\times}4$, extremal type.

• 대한수학회보
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• 제58권4호
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• pp.939-958
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• 2021

Some properties of strongly Gorenstein C-projective, C-injective and C-flat modules are studied, mainly considering these properties under change of rings. Specifically, the completions of rings, the localizations and the polynomial rings are considered.

• 대한수학회논문집
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• 제23권3호
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• pp.453-459
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• 2008

We introduce a concept of continuous homomorphisms between Csaszar frames and show that the Cauchy completion in CsFrm gives rise to a coreflection in the category PCsFrm (resp. UCsFrm) consisting of proximal Csaszar frames and uniform continuous homomor-phisms (resp. uniform Csaszar frames and uniform continuous homomor-phisms).