• 제목/요약/키워드: finite R-module

검색결과 66건 처리시간 0.027초

INJECTIVE PROPERTY RELATIVE TO NONSINGULAR EXACT SEQUENCES

  • Arabi-Kakavand, Marzieh;Asgari, Shadi;Tolooei, Yaser
    • 대한수학회보
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    • 제54권2호
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    • pp.559-571
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    • 2017
  • We investigate modules M having the injective property relative to nonsingular modules. Such modules are called "$\mathcal{N}$-injective modules". It is shown that M is an $\mathcal{N}$-injective R-module if and only if the annihilator of $Z_2(R_R)$ in M is equal to the annihilator of $Z_2(R_R)$ in E(M). Every $\mathcal{N}$-injective R-module is injective precisely when R is a right nonsingular ring. We prove that the endomorphism ring of an $\mathcal{N}$-injective module has a von Neumann regular factor ring. Every (finitely generated, cyclic, free) R-module is $\mathcal{N}$-injective, if and only if $R^{(\mathbb{N})}$ is $\mathcal{N}$-injective, if and only if R is right t-semisimple. The $\mathcal{N}$-injective property is characterized for right extending rings, semilocal rings and rings of finite reduced rank. Using the $\mathcal{N}$-injective property, we determine the rings whose all nonsingular cyclic modules are injective.

$iSight^{(R)}$를 이용한 툴 홀더 스핀들의 변형 및 응력해석 (Stress and Deformation Analysis of a Tool Holder Spindle using $iSight^{(R)}$)

  • 권구홍;정원지
    • 한국정밀공학회지
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    • 제27권9호
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    • pp.103-110
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    • 2010
  • This paper presents the optimized approximation of finite element modeling for a complex tool holder spindle using both DOE (Design of Experiment) with Optimal Latin Hypercube (OLH) method and approximation modeling method with Radial Basis Function (RBF) neural network structure. The complex tool holder is used for holding a (milling/drilling) tool of a machine tool. The engineering problem of complex tool holder results from the twisting of spindle of tool holder. For this purpose, we present the optimized approximation of finite element modeling for a complex tool holder spindle using both DOE (Design of Experiment) with Optimal Latin Hypercube (OLH) method (specifically a module of $iSight^{(R)}$ FD-3.1) and approximation modeling method with Radial Basis Function (RBF) (another module of $iSight^{(R)}$ FD-3.1) neural network structure

ON DISCRETE GROUPS

  • Cho, Young-Hyun;Chung, Jae-Myung
    • 대한수학회논문집
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    • 제9권2호
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    • pp.271-274
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    • 1994
  • The concept of a continuous module is a generalization of that of an injective module, and conditions ($C_1$), (C$_2$) and ($C_3$) are given for this concept in [4]. In this paper, we study modules with properties that are dual to continuity. These will be called discrete and we discuss discrete abelian groups. Throughout R is a ring with identity, M is a module over R, G is an abelian group of finite rank, E is the ring of endomorphisms of G and S is the center of E. Dual to the notion of essential submodules, we define small submodules of a module M over R.(omitted)

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THE FINITE DIMENSIONAL PRIME RINGS

  • Koh, Kwangil
    • 대한수학회보
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    • 제20권1호
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    • pp.45-49
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    • 1983
  • If R is ring and M is a right (or left) R-module, then M is called a faithful R-module if, for some a in R, x.a=0 for all x.mem.M then a=0. In [4], R.E. Johnson defines that M is a prime module if every non-zero submodule of M is faithful. Let us define that M is of prime type provided that M is faithful if and only if every non-zero submodule is faithful. We call a right (left) ideal I of R is of prime type if R/I is of prime type as a R-module. This is equivalent to the condition that if xRy.subeq.I then either x.mem.I ro y.mem.I (see [5:3:1]). It is easy to see that in case R is a commutative ring then a right or left ideal of a prime type is just a prime ideal. We have defined in [5], that a chain of right ideals of prime type in a ring R is a finite strictly increasing sequence I$_{0}$.contnd.I$_{1}$.contnd....contnd.I$_{n}$; the length of the chain is n. By the right dimension of a ring R, which is denoted by dim, R, we mean the supremum of the length of all chains of right ideals of prime type in R. It is an integer .geq.0 or .inf.. The left dimension of R, which is denoted by dim$_{l}$ R is similarly defined. It was shown in [5], that dim$_{r}$R=0 if and only if dim$_{l}$ R=0 if and only if R modulo the prime radical is a strongly regular ring. By "a strongly regular ring", we mean that for every a in R there is x in R such that axa=a=a$^{2}$x. It was also shown that R is a simple ring if and only if every right ideal is of prime type if and only if every left ideal is of prime type. In case, R is a (right or left) primitive ring then dim$_{r}$R=n if and only if dim$_{l}$ R=n if and only if R.iden.D$_{n+1}$ , n+1 by n+1 matrix ring on a division ring D. in this paper, we establish the following results: (1) If R is prime ring and dim$_{r}$R=n then either R is a righe Ore domain such that every non-zero right ideal of a prime type contains a non-zero minimal prime ideal or the classical ring of ritght quotients is isomorphic to m*m matrix ring over a division ring where m.leq.n+1. (b) If R is prime ring and dim$_{r}$R=n then dim$_{l}$ R=n if dim$_{l}$ R=n if dim$_{l}$ R<.inf. (c) Let R be a principal right and left ideal domain. If dim$_{r}$R=1 then R is an unique factorization domain.TEX>R=1 then R is an unique factorization domain.

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GRADED w-NOETHERIAN MODULES OVER GRADED RINGS

  • Wu, Xiaoying
    • 대한수학회보
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    • 제57권5호
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    • pp.1319-1334
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    • 2020
  • In this paper, we study the basic theory of the category of graded w-Noetherian modules over a graded ring R. Some elementary concepts, such as w-envelope of graded modules, graded w-Noetherian rings and so on, are introduced. It is shown that: (1) A graded domain R is graded w-Noetherian if and only if Rg𝔪 is a graded Noetherian ring for any gr-maximal w-ideal m of R, and there are only finite numbers of gr-maximal w-ideals including a for any nonzero homogeneous element a. (2) Let R be a strongly graded ring. Then R is a graded w-Noetherian ring if and only if Re is a w-Noetherian ring. (3) Let R be a graded w-Noetherian domain and let a ∈ R be a homogeneous element. Suppose 𝖕 is a minimal graded prime ideal of (a). Then the graded height of the graded prime ideal 𝖕 is at most 1.

GEOMETRIC REPRESENTATIONS OF FINITE GROUPS ON REAL TORIC SPACES

  • Cho, Soojin;Choi, Suyoung;Kaji, Shizuo
    • 대한수학회지
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    • 제56권5호
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    • pp.1265-1283
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    • 2019
  • We develop a framework to construct geometric representations of finite groups G through the correspondence between real toric spaces $X^{\mathbb{R}}$ and simplicial complexes with characteristic matrices. We give a combinatorial description of the G-module structure of the homology of $X^{\mathbb{R}}$. As applications, we make explicit computations of the Weyl group representations on the homology of real toric varieties associated to the Weyl chambers of type A and B, which show an interesting connection to the topology of posets. We also realize a certain kind of Foulkes representation geometrically as the homology of real toric varieties.

방진을 고려한 항공 정찰용 카메라 모듈부의 진동특성에 관한 연구 (A Study on the Vibration Characteristics of Camera Module for Aerial Reconnaissance Considering Vibration Isolator)

  • 이상은;이태원
    • 한국정밀공학회지
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    • 제29권5호
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    • pp.545-553
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    • 2012
  • A Gimbal structure system in observation reconnaissance aircraft is made up of camera module and stabilization drive device supporting camera module. During flight for image recording, the aircraft undergoes serious accelerations with wide frequencies due to several factors. Though base excitation of stabilization drive device induces vibration of camera module, it must get the stable and clean images. To achieve this aim, acceleration of camera module must be reduced. Hence, vibration isolators were installed to stabilization drive device. Considering isolators and bearings in the stabilization drive device, vibration characteristics of gimbal structure system were analyzed by finite element method. For three translational direction, acceleration transmissibility of camera module was calculated by harmonic responses analysis in the frequency range of 5 ~ 500 Hz. In addition to, sine-sweep experiment were performed to prove correctness of present analysis.

Development of the Caliper System for a Geometry PIG Based on Magnetic Field Analysis

  • Kim, Dong-Kyu;Cho, Sung-Ho;Park, Seoung-Soo;Yoo, Hui-Ryong;Park, Yong-Woo;Kho, Young-Tai;Park, Gwan-Soo;Park, Sang-Ho
    • Journal of Mechanical Science and Technology
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    • 제17권12호
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    • pp.1835-1843
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    • 2003
  • This paper introduces the development of the caliper system for a geometry PIG (Pipeline Inspection Gauge). The objective of the caliper system is to detect and measure dents, wrinkles, and ovalities affect the pipe structural integrity. The developed caliper system consists of a finger arm, an anisotropic permanent magnet, a back yoke, pins, pinholes and a linear hall effect sensor. The angle displacement of the finger arm is measured by the change of the magnetic field in sensing module. Therefore the sensitivity of the caliper system mainly depends on the magnitude of the magnetic field inside the sensing module. In this research, the ring shaped anisotropic permanent magnet and linear hall effect sensors were used to produce and measure the magnetic field. The structure of the permanent magnet, the back yoke and pinhole positions were optimized that the magnitude of the magnetic field range between a high of 0.1020 Tesla and a low of zero by using three dimensional nonlinear finite element methods. A simulator was fabricated to prove the effectiveness of the developed caliper system and the computational scheme using the finite element method. The experimental results show that the developed caliper system is quite efficient for the geometry PIG with good performance.

항공기 결빙 예측을 위한 Eulerian 기반 액적 충돌 및 결빙 증식 코드 (AN EULERIAN-BASED DROPLET IMPINGEMENT AND ICE ACCRETION CODE FOR AIRCRAFT ICING PREDICTION)

  • 정성기;명노신;조태환
    • 한국전산유체공학회지
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    • 제15권2호
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    • pp.71-78
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    • 2010
  • As a step toward accurate prediction of droplet impingement and ice accretion on aircraft, an Eulerian-based droplet impingement and ice accretion code for air flows around an airfoil containing water droplets is developed. A CFD solver based on the finite volume method was also developed to solve the clean airflow. The finite-volume-based approach for simulating droplet impingement on an airfoil was employed owing to its compatibility with the CFD solver and robustness. For ice accretion module, a simple model based on the control volume is combined with the droplet impingement module that provides the collection efficiency. To validate the present code, it is compared with NASA Glenn IRT (Icing Research Tunnel) experimental data and other well-known icing codes such as LEWICE and FENSAP-ICE. It is shown that the collection efficiency and shape of ice accretion are in good agreement with previous experimental and simulation results.