• Honam Mathematical Journal
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• v.21 no.1
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• pp.1-12
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• 1999

The height of a prime submodule and a module version of the Krull dimension are studied.

• Proceedings of the Materials Research Society of Korea Conference
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• 1996.11a
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• pp.143-143
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• 1996

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.727-733
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• 1998

In this short paper we shall find some properties on multiplication modules and prove three theorems.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.30 no.5
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• pp.325-330
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• 2017

We fabricated 1-D and 2-D diffraction gratings of SiOx anti-reflection (AR) film grown on a quartz substrate and integrated them into a c-Si photovoltaic (PV) submodule. The light-trapping effect of the resulting submodules was studied in terms of the oblique optical incident angle, ${\theta}_i$. As the ${\theta}_i$ increased, solar conversion efficiency, ${\eta}$, was improved as expected by the increased optical transmission caused by the grating. For ${\theta}_i{\leq}30^{\circ}$, the relative solar conversion efficiency, ${\Delta}{\eta}$, of a 1-D SiOx (t=300 nm) grating, compared to that of a flat SiOx AR-coated integrated PV submodule, was improved very little, with a small variation of within 2%, but increased markedly for ${\theta}_i{\geq}40^{\circ}$. We observed a change of ${\Delta}{\eta}$ as large as 10.7% and 9.5% for the SiOx grating of period t=800 nm and 1200 nm, respectively. For a 2-D SiOx (t=300 nm) grating integrated PV submodule, however, the optical trapping behavior was similar in terms of ${\theta}_i$ but its variation was small, within ${\pm}1.0%$.

• East Asian mathematical journal
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• v.6 no.2
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• pp.167-182
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• 1990

The relationships between submodules of a module and ideals of the endomorphism ring of a module had been studied in [1]. For a submodule L of a moudle M, the set $I^L$ of all endomorphisms whose images are contained in L is a left ideal of the endomorphism ring End (M) and for a submodule N of M, the set $I_N$ of all endomorphisms whose kernels contain N is a right ideal of End (M). In this paper, author defines an H-invariant module and proves that every submodule of an H-invariant module is the image and kernel of unique endomorphisms. Every ideal $I^L(I_N)$ of the endomorphism ring End(M) when M is H-invariant is a left (respectively, right) principal ideal of End(M). From the above results, if a module M is H-invariant then each left, right, or both sided ideal I of End(M) is an intersection of a left, right, or both sided principal ideal and I itself appropriately. If M is an H-invariant module then the ACC on the set of all left ideals of type $I^L$ implies the ACC on M. Also if the set of all right ideals of type $I^L$ has DCC, then H-invariant module M satisfies ACC. If the set of all left ideals of type $I^L$ satisfies DCC, then H-invariant module M satisfies DCC. If the set of all right ideals of type $I_N$ satisfies ACC then H-invariant module M satisfies DCC. Therefore for an H-invariant module M, if the endomorphism ring End(M) is left Noetherian, then M satisfies ACC. And if End(M) is right Noetherian then M satisfies DCC. For an H-invariant module M, if End(M) is left Artinian then M satisfies DCC. Also if End(M) is right Artinian then M satisfies ACC.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.609-616
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• 2005

In this paper we show that we can extend the purity of left R-modules to the case of polynomial modules, bipolynomial modules, and also inverse polynomial modules.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.739-746
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• 2010

In this short paper, we show that properties of an ideal I of a ring R are related to those of the homogeneous ideal I(+)IM of a ring R(+)M.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.429-436
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• 2009

In this short paper, we prove some new properties on homogeneous ideals and primary ideals of R(+)M.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.569-575
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• 2007

Let M be a nonzero module. M has the property that every submodule of M lies over a direct summand of M. We study some properties of such a module. The endomorphism ring of such a module is also studied. The relationships of such a module to the semi-regular modules, and to the semi-perfect modules are described.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.475-483
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• 2017

In this paper we consider the tight closure of an ideal relative to a module whose its zero submodule has a primary decomposition.