• Title/Summary/Keyword: Fundamental Modules

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COHEN-MACAULAY MODULES OVER NOETHERIAN LOCAL RINGS

  • Bahmanpour, Kamal
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.2
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    • pp.373-386
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    • 2014
  • Let (R,m) be a commutative Noetherian local ring. In this paper we show that a finitely generated R-module M of dimension d is Cohen-Macaulay if and only if there exists a proper ideal I of R such that depth($M/I^nM$) = d for $n{\gg}0$. Also we show that, if dim(R) = d and $I_1{\subset}\;{\cdots}\;{\subset}I_n$ is a chain of ideals of R such that $R/I_k$ is maximal Cohen-Macaulay for all k, then $n{\leq}{\ell}_R(R/(a_1,{\ldots},a_d)R)$ for every system of parameters $a1,{\ldots},a_d$ of R. Also, in the case where dim(R) = 2, we prove that the ideal transform $D_m(R/p)$ is minimax balanced big Cohen-Macaulay, for every $p{\in}Assh_R$(R), and we give some equivalent conditions for this ideal transform being maximal Cohen-Macaulay.

ON THE LOCAL COHOMOLOGY OF MINIMAX MODULES

  • Mafi, Amir
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.6
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    • pp.1125-1128
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    • 2011
  • Let R be a commutative Noetherian ring, a an ideal of R, and M a minimax R-module. We prove that the local cohomology modules $H^j_a(M)$ are a-cominimax; that is, $Ext^i_R$(R/a, $H^j_a(M)$) is minimax for all i and j in the following cases: (a) dim R/a = 1; (b) cd(a) = 1, where cd is the cohomological dimension of a in R; (c) dim $R{\leq}2$. In these cases we also prove that the Bass numbers and the Betti numbers of $H^j_a(M)$ are finite.

LOCAL-GLOBAL PRINCIPLE AND GENERALIZED LOCAL COHOMOLOGY MODULES

  • Bui Thi Hong Cam;Nguyen Minh Tri;Do Ngoc Yen
    • Communications of the Korean Mathematical Society
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    • v.38 no.3
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    • pp.649-661
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    • 2023
  • Let 𝓜 be a stable Serre subcategory of the category of R-modules. We introduce the concept of 𝓜-minimax R-modules and investigate the local-global principle for generalized local cohomology modules that concerns to the 𝓜-minimaxness. We also provide the 𝓜-finiteness dimension f𝓜I (M, N) of M, N relative to I which is an extension the finiteness dimension fI (N) of a finitely generated R-module N relative to I.

A Study on Reformability and Application of Tensegrity Modules (텐서그러티 모듈의 변형 및 응용에 관한 연구)

  • Choi, Sun-Young;Park, Sun-Woo;Park, Chan-Soo
    • Journal of Korean Association for Spatial Structures
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    • v.5 no.2 s.16
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    • pp.73-79
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    • 2005
  • Tensegrity is a relatively new structural system based on the use of continuous tension-discontinuous compression. Of course, a much more detailed structural investigation would be necessary, but at least in order to achieve the intended purpose, it is essential to understand the structural principles and the fundamental forces of tensegrity. Once this point is established, the applications of them to architecture are described, as well as the characteristics of these structures. Then, in spite of the controversial definitions to explain these systems, several examples of tensegrity prototypes or modules constructed in iESD(Institute of Environmental Structure Design) are presented to illustrate the feasibility of tensegrity as a lightweight structure. In this work, consequently, the reformability and application of tensegrity modules have also been researched in architecture, after the patterns of basic module as well as fundamental definition are introduced.

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The Fundamental Researches to Evaluate PVT Module Performance (PVT 모듈 성능 평가를 위한 기초 연구)

  • Kim, Pilkyu
    • Journal of the Korean Solar Energy Society
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    • v.38 no.4
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    • pp.1-9
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    • 2018
  • PVT modules commonly can be defined as a combination of PV modules and thermal collectors. After absorbing sun light, electricity and hot water can be actually provided to users simultaneously, which dual outputs (electricity and hot water) have drawn academic interest and industrial activities. Additionally, heat exchange between solar cell and flowing water can enhance solar cell efficiency. Because of PVT modules effectiveness, new international markets and commercial products have made. Especially European, facilities and measurement methods are established to evaluate PVT module performance. However, there are no currently appropriate internationally and domestic standards and facilities to test PVT module performance Herein, to test PVT module performance, indoor thermal simulators and fundamental standard study are considered.

Low-Frequency Electromagnetic Leakage Signal Analysis According to Fundamental Operations of Smartphones (스마트폰 기본 동작 모드에 따른 저주파 대역 누설 전자파 신호 특성 분석)

  • Lee, Young-Jun;Park, Heesun;Kwon, YoungHyoun;Lee, Jaeki;Choi, Ji-Eun;Cho, Sangwoo
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.41 no.9
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    • pp.1108-1119
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    • 2016
  • This paper presents the spectral analysis and radiation pattern of low-frequency electromagnetic(EM) leakage signals according to the fundamental operations of smartphones. The EM leakage signals generated by the activation of four I/O sensor modules such as a touch-screen, a camera, a microphone and a speaker are captured by the commercial near-field magnetic probe with 1cm spatial resolution. The analysis results show that the leakage of the EM wave occurs strongly around the activated I/O sensor modules, AP(Application Processor) and memory modules. Also, the distinguishable frequency characteristic is shown in each spectrum of EM leakage signals.

PRIME M-IDEALS, M-PRIME SUBMODULES, M-PRIME RADICAL AND M-BAER'S LOWER NILRADICAL OF MODULES

  • Beachy, John A.;Behboodi, Mahmood;Yazdi, Faezeh
    • Journal of the Korean Mathematical Society
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    • v.50 no.6
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    • pp.1271-1290
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    • 2013
  • Let M be a fixed left R-module. For a left R-module X, we introduce the notion of M-prime (resp. M-semiprime) submodule of X such that in the case M=R, it coincides with prime (resp. semiprime) submodule of X. Other concepts encountered in the general theory are M-$m$-system sets, M-$n$-system sets, M-prime radical and M-Baer's lower nilradical of modules. Relationships between these concepts and basic properties are established. In particular, we identify certain submodules of M, called "primeM-ideals", that play a role analogous to that of prime (two-sided) ideals in the ring R. Using this definition, we show that if M satisfies condition H (defined later) and $Hom_R(M,X){\neq}0$ for all modules X in the category ${\sigma}[M]$, then there is a one-to-one correspondence between isomorphism classes of indecomposable M-injective modules in ${\sigma}[M]$ and prime M-ideals of M. Also, we investigate the prime M-ideals, M-prime submodules and M-prime radical of Artinian modules.

RINGS AND MODULES WHICH ARE STABLE UNDER NILPOTENTS OF THEIR INJECTIVE HULLS

  • Nguyen Thi Thu Ha
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.2
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    • pp.339-348
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    • 2023
  • It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right R-module is nilpotent-invariant. We prove that R ≅ R1 × R2, where R1, R2 are rings which satisfy R1 is a semi-simple Artinian ring and R2 is square-free as a right R2-module and all idempotents of R2 is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right R-modules. Such a module is shown to have isomorphic simple modules eR and fR, where e, f are orthogonal primitive idempotents such that eRf ≠ 0.

A Stipulation Based Sources Insertion Multilevel Inverter (SBSIMLI) for Waning the Component Count and Separate DC Sources

  • Edwin, Jose S;Titus, S
    • Journal of Electrical Engineering and Technology
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    • v.12 no.4
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    • pp.1519-1528
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    • 2017
  • The paper proposes a well structured, component count waned single phase multilevel inverter (MLI) topology, which drives three different modules viz. Stipulation Based Sources Insertion (SBSI) module, Level Count Increasing (LCI) module and Inter-Linking H-Bridge (ILHB) module. The SBSI module confronts the number of basic sources needed in series/parallel to achieve required magnitude for any particular level. The LCI possesses an offsetting dc source and opuses to increase the number of levels and the ILHB module links the SBSI and LCI modules. A developed Hybrid Pulse Width Modulation (HPWM) strategy has PWM pulses for the switches of LCI module while the switches of the remaining two modules function at fundamental switching frequency. A fifteen level version of the proposed stipulation based sources insertion MLI (SBSIMLI) topology is simulated in MATLAB R2010a and a prototype of the similar specifications is constructed to validate the performance by experimental results. The comparison between the developed SBSIMLI topology and the competent topologies shows many interesting facts.

A Study on Concentrating Photovoltaic Module with Plate Structure (평판 구조의 집광형 태양광 모듈 구조에 관한 연구)

  • Park, Seung-Jae;Hong, Min-Sung
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.22 no.4
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    • pp.629-634
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    • 2013
  • This study aims to investigate a new structure for a concentrating photovoltaic (PV) module using a III-V compound semiconductor solar cellto solve the problems of existing concentrating PV modules and to explore a concentrating optical system with a flat structure, which shows remarkable advantages in terms of manufacturing cost, installation, and maintenance. This study should greatly contribute toward the development of concentrating PV modules. This study was performed to achieve an improvement in efficiency and economy and to implement an actual product. A new source of renewable energy is the only way in which countries that cannot produce oil can even emerge as an energy power. Therefore, this work can serve as a fundamental study that will help South Korea grow into a country that is a PV power generation force.