• Honam Mathematical Journal
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• v.37 no.2
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• pp.187-205
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• 2015

We discuss the relationship between interval-valued fuzzy ideals and interval-valued fuzzy congruence on a distributive lattice L and show that for a generalized Boolean algebra the lattice of interval-valued fuzzy ideals is isomorphic to the lattice of interval-valued fuzzy congruences. Finally we consider the products of interval-valued fuzzy ideals and obtain a necessary and sufficient condition for an interval-valued fuzzy ideal on the direct sum of lattices to be representable as a direct sum of interval-valued fuzzy ideals on each lattice.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.403-414
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• 2016

Let R be a ring, and let M be a left R-module. If M is Rad-supplementing, then every direct summand of M is Rad-supplementing, but not each factor module of M. Any finite direct sum of Rad-supplementing modules is Rad-supplementing. Every module with composition series is (Rad-)supplementing. M has a Rad-supplement in its injective envelope if and only if M has a Rad-supplement in every essential extension. R is left perfect if and only if R is semilocal, reduced and the free left R-module $(_RR)^{({\mathbb{N})}$ is Rad-supplementing if and only if R is reduced and the free left R-module $(_RR)^{({\mathbb{N})}$ is ample Rad-supplementing. M is ample Rad-supplementing if and only if every submodule of M is Rad-supplementing. Every left R-module is (ample) Rad-supplementing if and only if R/P(R) is left perfect, where P(R) is the sum of all left ideals I of R such that Rad I = I.

• Journal of Ocean Engineering and Technology
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• v.13 no.4 s.35
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• pp.169-173
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• 1999

In this paper some modifications for Lu's inverse method of fairing process are presented. The object function is changed and additional constraints for hull curve foiling is proposed. The newly introduced minimizing object function is the sum of the distances between the two curve's positions at the same parameter values instead of the sum of the distances between two vertices. The new one is better to represent the physical meaning of the object function, the smaller differences between two curves. In ship hull fairing the end tangent of curve has to be fined in some cases, so the additional constraint is considered to preserve the direction of end tangent. The sample results are shown.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1033-1039
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• 2011

Let R be a ring with identity 1, I(R) be the set of all idempotents in R and G be the group of all units of R. In this paper, we show that for any semiperfect ring R in which 2 = 1+1 is a unit, I(R) is closed under multiplication if and only if R is a direct sum of local rings if and only if the set of all minimal idempotents in R is closed under multiplication and eGe is contained in the group of units of eRe. In particular, for a left Artinian ring in which 2 is a unit, R is a direct sum of local rings if and only if the set of all minimal idempotents in R is closed under multiplication.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.37-43
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• 2006

We prove that $M_1\longrightarrow^f\;M_2$ is an injective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ if and only if $M_1\;and\;M_2$ are injective left R-modules, $M_1\longrightarrow^f\;M_2$ is isomorphic to a direct sum of representation of the types $E_l{\rightarrow}0$ and $M_1\longrightarrow^{id}\;M_2$ where $E_l\;and\;E_2$ are injective left R-modules. Then, we generalize the result so that a representation$M_1\longrightarrow^{f_1}\;M_2\; \longrightarrow^{f_2}\;\cdots\;\longrightarrow^{f_{n-1}}\;M_n$ of a quiver $Q={\bullet}{\rightarrow}{\bullet}{\rightarrow}{\cdots}{\rightarrow}{\bullet}$ is an injective representation if and only if each $M_i$ is an injective left R-module and the representation is a direct sum of injective representations.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.372-377
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• 2004

We introduce the concepts of intuitionistic fuzzy ideals and intuitionistic fuzzy congruences on a lattice, and discuss the relationship between intuitionistic fuzzy ideals and intuitionistic fuzzy congruence on a distributive lattice. Also we prove that for a generalized Boolean algebra, the lattice of intuitionistic fuzzy ideals is isomorphic to the lattice of intuitionistic fuzzy congruences. Finally, we consider the products of intuitionistic fuzzy ideals and obtain a necessary and sufficient condition for an intuitionistic fuzzy ideals on the direct sum of lattices to be representable on a direct sum of intuitionistic fuzzy ideals on each lattice.

• Journal of KIISE:Databases
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• v.30 no.6
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• pp.553-560
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• 2003

A range-sum query is very popular and becomes important in finding trends and in discovering relationships between attributes in diverse database applications. It sums over the selected cells of an OLAP data cube where target cells are decided by specified query ranges. The direct method to access the data cube itself forces too many cells to be accessed, therefore it incurs severe overheads. The prefix-sum cube was proposed for the efficient processing of range-sum queries in OLAP environments. However, the prefix-sum cube has been criticized due to its space requirement. In this paper, we propose a lossless compression method called the overlapped-subcube that is developed for the purpose of compressing prefix-sum cubes. A distinguished feature of the overlapped-subcube is that searches can be done without decompressing. The overlapped-subcube reduces the space requirement for storing prefix-sum cubes, and improves the query performance.

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.549-568
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• 2007

In this paper we obtain a decomposition of certain factors of the signed Brauer algebra into a direct sum of simple algebras and we obtain the structure of the factor algebra.

• Honam Mathematical Journal
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• v.3 no.1
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• pp.109-113
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• 1981

본(本) 논문(論文)에서는 Noetherian Ring 상(上)의 finitely generated injective module이 completely indecomposable modules의 direct sum으로 표시(表示)될 필요충분조건(必要充分條件)을 구(求)하였다.

• Kyungpook Mathematical Journal
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• v.32 no.3_spc
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• pp.415-420
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• 1992