• 대한수학회보
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• 제36권4호
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• pp.693-699
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• 1999

It is a well-known result that a commutative ring R is von Neumann regular if and only if for any maximal ideal m of R the R-module R/m is flat. In this note we bring a generalization of this result for modules.

• 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.

• 호남수학학술지
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• 제41권4호
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• pp.799-812
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• 2019

We introduce flat e-covers of modules and define e-perfect rings as a generalization of perfect rings. We prove that a ring is right perfect if and only if it is semilocal and right e-perfect which generalizes a result due to N. Ding and J. Chen. Moreover, in the light of the fact that a ring R is right perfect if and only if flat covers of any R-module are projective covers, we study on the rings over which flat covers of modules are (generalized) locally projective covers, and obtain some characterizations of (semi) perfect, A-perfect and B-perfect rings.

• 한국태양에너지학회 논문집
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• 제31권6호
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• pp.32-39
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• 2011

This study is about the installation of the solar cell modules. The solar cell modules are built by the tree-mimic structure, and the performance is compared with that of the flat-plate type solar cell module installation. The mathematical tree model, which was suggested by Fisher and Honda, is utilized to determine the location of the solar cell modules for the tree-mimic type. The experiment shows that the generated electric power of the flat-plate type is higher than that of the tree-mimic type by 30% for one month of July. This lower performance for the tree-mimic type comes from the shading effects among the solar cell modules. The theoretical calculation for the absorbed solar radiation on the two types of solar cell installation shows that the tree-mimic type is higher than the flat-plate type by 8.5%. The shading area for the tree-mimic model is calculated with time by using the 3D-CAD, which will be utilized for the optimization of the tree-mimic model in the future.

• 대한수학회지
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• 제54권4호
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• pp.1281-1299
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• 2017

A submodule N of a module M is called ${\mathcal{S}}$-closed (in M) if M/N is nonsingular. It is well-known that the class Closed of short exact sequences determined by closed submodules is a proper class in the sense of Buchsbaum. However, the class $\mathcal{S}-Closed$ of short exact sequences determined by $\mathcal{S}$-closed submodules need not be a proper class. In the first part of the paper, we describe the smallest proper class ${\langle}\mathcal{S-Closed}{\rangle}$ containing $\mathcal{S-Closed}$ in terms of $\mathcal{S}$-closed submodules. We show that this class coincides with the proper classes projectively generated by Goldie torsion modules and coprojectively generated by nonsingular modules. Moreover, for a right nonsingular ring R, it coincides with the proper class generated by neat submodules if and only if R is a right SI-ring. In abelian groups, the elements of this class are exactly torsionsplitting. In the second part, coprojective modules of this class which we call ec-flat modules are also investigated. We prove that injective modules are ec-flat if and only if each injective hull of a Goldie torsion module is projective if and only if every Goldie torsion module embeds in a projective module. For a left Noetherian right nonsingular ring R of which the identity element is a sum of orthogonal primitive idempotents, we prove that the class ${\langle}\mathcal{S-Closed}{\rangle}$ coincides with the class of pure-exact sequences of modules if and only if R is a two-sided hereditary, two-sided $\mathcal{CS}$-ring and every singular right module is a direct sum of finitely presented modules.

• 전자공학회논문지D
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• 제34D권3호
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• pp.25-33
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• 1997

In the design of microwave multi-stage amplifiers composed of N amplifier modules, the variation of performances of amplifier as various connection length between modules has been studied. In addition, the methods, equations and conditions for the maximum gain or the most flat gain are presented. The results of sensitivity analysis for the connection length showed that the small change in phase of input, output reflection coefficients(S$_{11}$, S$_{22}$) of module itself is the most important in determination of connection length for the most flat gain. Th egain flatness of 2-module amplifier of which connection length between modules had been determined by presented methods was the best one out of performances with various arbitrary connectio lengths.s.

• 대한수학회보
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• 제59권3호
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• pp.643-657
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• 2022

Let R be a ring and S a multiplicative subset of R. An R-module T is called u-S-torsion (u-always abbreviates uniformly) provided that sT = 0 for some s ∈ S. The notion of u-S-exact sequences is also introduced from the viewpoint of uniformity. An R-module F is called u-S-flat provided that the induced sequence 0 → A ⊗_R F → B ⊗_R F → C ⊗_R F → 0 is u-S-exact for any u-S-exact sequence 0 → A → B → C → 0. A ring R is called u-S-von Neumann regular provided there exists an element s ∈ S satisfying that for any a ∈ R there exists r ∈ R such that sα = rα². We obtain that a ring R is a u-S-von Neumann regular ring if and only if any R-module is u-S-flat. Several properties of u-S-flat modules and u-S-von Neumann regular rings are obtained.

• 대한수학회지
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• 제47권4호
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• pp.691-704
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• 2010

Over a ring R, let $P_R$ be a finitely generated projective right R-module. Then we define the G-injector (G-projector) if $P_R$ preservers Gorenstein injective modules (Gorenstein projective modules), the Gflator if $P_R$ preservers Gorenstein flat modules. G-injector (G-flator) and G-injector are characterized focus primarily on the cases where R is a Gorenstein ring, and under this condition we also study the relations between the injector (projector, flator) and the G-injector (G-projector, G-flator). Over any ring we also give the characteristics of G-injector (G-flator) by the Gorenstein injective (Gorenstein flat) dimensions of modules.

• 대한수학회지
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• 제50권1호
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• pp.219-229
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• 2013

Let R be a commutative ring with $1{\neq}0$ and let $\mathcal{H}$ = {R|R is a commutative ring and Nil(R) is a divided prime ideal}. If $R{\in}\mathcal{H}$, then R is called a ${\phi}$-ring. In this paper, we introduce the concepts of ${\phi}$-torsion modules, ${\phi}$-flat modules, and ${\phi}$-von Neumann regular rings.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2002년도 춘계학술대회 논문집 유기절연재료 전자세라믹 방전플라즈마 일렉트렛트 및 응용기술
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• pp.15-17
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• 2002

Leakage inductance and temperature rise are two of the more impotent problems facing the magnetic core technology of today's high frequency transformers. Excessive leakage inductance increases the stress on the switching transistors and limits the duty-cycle, and excessive temperature rise can lead the design limitation of high frequency transformer with high current. The flat transformer technology provides a very good solution to the problems of leakage inductance and thermal management for high frequency power. The critical magnetic components and windings are optimized and packaged within a completely assembled module. The turns ratio in a flat transformer is determined as the product of the number of elements or modules times the number of primary turns. The leakage inductance increase proportionately to the number of elements, but since it is reduced as the square of the turns, the net reduction can be very significant. The flat transformer modules use cores which have no gap. This eliminates fringing fluxes and stray flux outside of the core. The secondary windings are formed of flat metal and are bonded to the inside surface of the core. The secondary winding thus surrounds the primary winding, so nearly all of the flux is captured.