• Proceedings of the KIEE Conference
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• 2003.07c
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• pp.1713-1715
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• 2003

This paper describes an LED module for a desk lamp using 1[W] high flux while LEDs. The optimum length of the module is obtained from the lighting simulation of the target area of $500{\times}500[mm]$ on the desk, which in turn determines an optimum separation between LEDs. The main issue is to find the optimum separation which gives good illuminance uniformity and high coefficient of utilization at at various reflector structures. Two module configuations of linear and ring types are compared. As a result, good illuminance uniformity is obtained in the case of the ring module. The mofied twin type, however, gives better performance than the ring module, and shows the most performance at an separation angle of around $30^{\circ}$.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.453-467
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• 2000

For any S-flat module RM(which will be called endoflat) with a commutaitve ring R with identity, where S is the endomorphism ring RM, the fact that every epimorphism is an automorphism has been proved and the Jacobson Radical Rad(S) of S is described as follow; Rad(S) = { f$\in$S｜Imf=Mf is small in M} = {f$\in$S｜Imf $\leq$Rad(M)}. Additionally for any quasi-injective endo-flat module RM, the fact that every monomorphism is an automorphism has been proved and the Jacobson Radical Rad(S) for any quasi-injective endo-flat module has been studied too. Also some equivalent conditions for the semi-primitivity of any faithful endo-flat module RM with the open Jacobson Radical Rad(M) and those for the semi-simplicity of any faithful endo-flat quasi-injective module RM with the closed Socle Soc(M) have been studied.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1483-1494
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• 2021

Let A and B be rings and U be a (B, A)-bimodule. If _BU has finite flat dimension, U_A has finite flat dimension and U ⊗_A C is a cotorsion left B-module for any cotorsion left A-module C, then the Gorenstein flat-cotorsion modules over the formal triangular matrix ring $T=\(\array{A&0\\U&B}\)$ are explicitly described. As an application, it is proven that each Gorenstein flat-cotorsion left T-module is flat-cotorsion if and only if every Gorenstein flat-cotorsion left A-module and B-module is flat-cotorsion. In addition, Gorenstein flat-cotorsion dimensions over the formal triangular matrix ring T are studied.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.311-314
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• 1996

Let G be an abelian group of finite rink and E be the endomorphism ring of G. Then G is a left E-module by defining $f\cdota = f(a)$ for $f \in E$ and $a \in G$. In this case a condition for an E-module G to be regular is given.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.45-51
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• 2018

This paper contains some results that grew out of an attempt to Camillo-Krause conjecture: Is a ring R right Noetherian if for each nonzero right ideal I of R, R/I is an Artinian right R-module?

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.599-608
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• 1999

$H_v$-rings first were introduced by Vougiouklis in 1990. Then Darafsheh and the present author defined the $H_v$-ring of fractions $S_{-1}R$ of a commutative hyperring. The largest class of multivalued systems satisfying the module-like axioms is the Hv-module. In this paper we define $H_v$-module of fractions of a hypermodule. Some interesting results concerning this $H_v$-module is proved.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.23-33
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• 2011

Extending the notion of McCoy rings, we introduce the class of McCoy modules. Over a given ring R, it contains the class of Armendariz modules (over R). Some properties of this class of modules are established, and equivalent conditions for McCoy modules are given. Moreover, we study the relationship between a module and its polynomial module. Several known results relating to McCoy rings can be obtained as corollaries of our results.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.729-741
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• 2019

In this paper we give a full characterization of prime submodules of a finitely generated projective module M over a commutative ring R with identity. Also we study the existence of primary decomposition of a submodule of a finitely generated projective module and characterize the minimal primary decomposition of this submodule. Finally, we characterize the radical of an arbitrary submodule of a finitely generated projective module M and study submodules of M which satisfy the radical formula.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.611-622
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• 2010

A ring R is called left max-coherent provided that every maximal left ideal is finitely presented. $\mathfrak{M}\mathfrak{I}$ (resp. $\mathfrak{M}\mathfrak{F}$) denotes the class of all max-injective left R-modules (resp. all max-flat right R-modules). We prove, in this article, that over a left max-coherent ring every right R-module has an $\mathfrak{M}\mathfrak{F}$-preenvelope, and every left R-module has an $\mathfrak{M}\mathfrak{I}$-cover. Furthermore, it is shown that a ring R is left max-injective if and only if any left R-module has an epic $\mathfrak{M}\mathfrak{I}$-cover if and only if any right R-module has a monic $\mathfrak{M}\mathfrak{F}$-preenvelope. We also give several equivalent characterizations of MI-injectivity and MI-flatness. Finally, $\mathfrak{M}\mathfrak{I}$-dimensions of modules and rings are studied in terms of max-injective modules with the left derived functors of Hom.

• 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.