• Title/Summary/Keyword: generated set for modules

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INDEPENDENTLY GENERATED MODULES

  • Kosan, Muhammet Tamer;Ozdin, Tufan
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.5
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    • pp.867-871
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    • 2009
  • A module M over a ring R is said to satisfy (P) if every generating set of M contains an independent generating set. The following results are proved; (1) Let $\tau$ = ($\mathbb{T}_\tau,\;\mathbb{F}_\tau$) be a hereditary torsion theory such that $\mathbb{T}_\tau$ $\neq$ Mod-R. Then every $\tau$-torsionfree R-module satisfies (P) if and only if S = R/$\tau$(R) is a division ring. (2) Let $\mathcal{K}$ be a hereditary pre-torsion class of modules. Then every module in $\mathcal{K}$ satisfies (P) if and only if either $\mathcal{K}$ = {0} or S = R/$Soc_\mathcal{K}$(R) is a division ring, where $Soc_\mathcal{K}$(R) = $\cap${I 4\leq$ $R_R$ : R/I$\in\mathcal{K}$}.

ON FRAMES FOR COUNTABLY GENERATED HILBERT MODULES OVER LOCALLY C*-ALGEBRAS

  • Alizadeh, Leila;Hassani, Mahmoud
    • Communications of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.527-533
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    • 2018
  • Let $\mathcal{X}$ be a countably generated Hilbert module over a locally $C^*$-algebra $\mathcal{A}$ in multiplier module M($\mathcal{X}$) of $\mathcal{X}$. We propose the necessary and sufficient condition such that a sequence $\{h_n:n{{\in}}\mathbb{N}\}$ in M($\mathcal{X}$) is a standard frame of multipliers in $\mathcal{X}$. We also show that if T in $b(L_{\mathcal{A}}(\mathcal{X}))$, the space of bounded maps in set of all adjointable maps on $\mathcal{X}$, is surjective and $\{h_n:n{{\in}}\mathbb{N}\}$ is a standard frame of multipliers in $\mathcal{X}$, then $\{T{\circ}h_n:n{\in}\mathbb{N}}$ is a standard frame of multipliers in $\mathcal{X}$, too.

A Study for Process Planning of Progressive Working by the using of Fuzzy Set Theory (Fuzzy set 이론을 이용한 프로그레시브 가공의 공정설계에 관한 연구)

  • Kim, Y. M.;Kim, J. H.;Kim, C.;Choi, J. C.
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2001.04a
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    • pp.735-739
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    • 2001
  • This paper describes a research work of developing computer-aided design of a product with bending and piercing for progressive working. An approach to the system for progressive working os based on the knowledge-based rules. Knowledge for the system is formulated from plasticity theorise, experimental results and the empirical knowledge of field experts. the system has been written in AutoLISP on the AutoCAD with a personal computer and is composed of three main modules, which are input and shape treatment, flat pattern layout and strip layout modules. Strip layout of the system is designed by using fuzzy set theory. Process planning is determinated by fuzzy value according to several rules. Strip layout drawing generated in strip layout module is presented in 3-D graphic forms, including bending sequences and piercing processes with punch profiles divided into for external area. Results obtained using the modules enable the manufacturer for progressive working of electric products to be more efficient in this field.

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ON FINITENESS PROPERTIES ON ASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES AND EXT-MODULES

  • Chu, Lizhong;Wang, Xian
    • Journal of the Korean Mathematical Society
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    • v.51 no.2
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    • pp.239-250
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    • 2014
  • Let R be a commutative Noetherian (not necessarily local) ring, I an ideal of R and M a finitely generated R-module. In this paper, by computing the local cohomology modules and Ext-modules via the injective resolution of M, we proved that, if for an integer t > 0, dim$_RH_I^i(M){\leq}k$ for ${\forall}i$ < t, then $$\displaystyle\bigcup_{i=0}^{j}(Ass_RH_I^i(M))_{{\geq}k}=\displaystyle\bigcup_{i=0}^{j}(Ass_RExt_R^i(R/I^n,M))_{{\geq}k}$$ for ${\forall}j{\leq}t$ and ${\forall}n$ >0. This shows that${\bigcup}_{n>0}(Ass_RExt_R^i(R/I^n,M))_{{\geq}k}$ is a finite set for ${\forall}i{\leq}t$. Also, we prove that $\displaystyle\bigcup_{i=1}^{r}(Ass_RM/(x_1^{n_1},x_2^{n_2},{\ldots},x_i^{n_i})M)_{{\geq}k}=\displaystyle\bigcup_{i=1}^{r}(Ass_RM/(x_1,x_2,{\ldots},x_i)M)_{{\geq}k}$ if $x_1,x_2,{\ldots},x_r$ is M-sequences in dimension > k and $n_1,n_2,{\ldots},n_r$ are some positive integers. Here, for a subset T of Spec(R), set $T_{{\geq}i}=\{{p{\in}T{\mid}dimR/p{\geq}i}\}$.

A New Method for Generating Structural Configurations of Modular-Reconfigurable Machine Tool (모듈러 RMT의 구조형태 생성을 위한 새로운 방법)

  • Choi Y. H.;Park H. M.;Jang S. H.;Choi E. Y.;Kim I. S.;Park J. K.
    • Proceedings of the Korean Society of Machine Tool Engineers Conference
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    • 2005.05a
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    • pp.435-440
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    • 2005
  • This study describes a new method of constructing Reconfigurable machine tools configurations from a set of modules or components. This proposed method defines combinability vector for each module and mutual combinability coefficient matrix for adjacent two modules. All of machine configurations possible to be generated from any two adjacent modules can be determined by quadratic form of two associated combinability vectors. Furthermore, all of possible RMT configurations generating from a series of multiple modules also can be obtained by multiplying quadratic form of two adjacent conbinability vectors recursively. Our proposed RMT configuration generating method can be successfully applied to determining all of possible machine configurations from several modules or components at conceptual- or preliminary- design stage.

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Development of a Process Sequence Determination Technique by Fuzzy Set Theory for Electric Product with Piercing and Bending Operations (퍼지셋을 이용한 퍼어싱 및 굽힘공정을 갖는 전기제품의 공정순서 결정기법 개발)

  • Kim J.H.;Kim Chul
    • Journal of the Korean Society for Precision Engineering
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    • v.22 no.9 s.174
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    • pp.137-146
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    • 2005
  • This paper describes a research work to develop a computer-aided design for the product made by progressive working of bending and piercing. An approach to the system for progressive working is based on the knowledge-based rules. Knowledge for the system is formulated from plasticity theories, experimental results and the empirical knowledge of field experts. The system has been written in AutoLISP on the AutoCAD with a personal computer and is composed of three main modules, which are input and shape treatment, flat pattern layout, strip layout modules. The system is designed by considering several factors, such as piercing and bending sequences by fuzzy set theory, complexities of blank geometry, punch profiles, and the availability of a press equipment. Strip layout drawing generated in the strip layout module is presented in 3-D graphic forms, including piercing and bending sequences with punch profiles divided into for external area. Results obtained using the modules enable the manufacturer for progressive working of electric products to be more efficient in this field.

A Study on Progressive Die Design by the using of Finite Element Method (유한요소법을 이용한 프로그레시브 금형 설계에 관한 연구)

  • Park, Chul-Woo;Kim, Young-Min;Kim, Chul;Kim, Young-Ho;Choi, Jae-Chan
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2002.05a
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    • pp.1012-1016
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    • 2002
  • This paper describes a research work of developing computer-aided design of a product with bending and piercing for progressive working. An approach to the system for progressive working is based on the knowledge-based rules. Knowledge for the system is formulated from plasticity theories, experimental results and the empirical knowledge of field experts. The system has been written in Auto-LISP on the Auto-CAD with a personal computer and is composed of four main modules, which are input and shape treatment, flat pattern layout, strip layout, and die layout modules. The system is designed by considering several factors, such as bending sequences by fuzzy set theory, complexities of blank geometry, punch profiles, and the availability of a press equipment. Strip layout drawing generated in the strip layout module is presented in 3-D graphic forms, including bending sequences and piercing processes with punch profiles divided into for external area. The die layout module carries out die design for each process obtained from the results of the strip layout. Results obtained using the modules enable the manufacturer for progressive working of electric products to be more efficient in this field.

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A Study on Progressive Working of Electric Product by the using of Fuzzy Set Theory (퍼지 셋 이론을 이용한 전기제품의 프로그레시브 가공에 관한 연구)

  • Kim, J. H;Kim, Y. M.;Kim, Chul;Choi, J. C.
    • Journal of the Korean Society for Precision Engineering
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    • v.19 no.1
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    • pp.79-92
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    • 2002
  • This paper describes a research work of developing computer-aided design of a product with bending and piercing for progressive working. An approach to the system for progressive working is based on the knowledge-based rules. Knowledge for the system is formulated from plasticity theories, experimental results and the empirical knowledge of field experts. The system has been written in AutoLISP on the AutoCAD with a personal computer and is composed of four main modules, which are input and shape treatment, flat pattern layout, strip layout and die layout modules. The system is designed by considering several factors, such as bending sequences by fuzzy set theory, complexities of blank geometry, punch profiles, and the availability of a press equipment. Strip layout drawing generated in the strip layout module is presented in 3-D graphic farms, including bending sequences and piercing processes with punch profiles divided into for external area. The die layout module carries out die design for each process obtained from the results of the strip layout. Results obtained using the modules enable the manufacturer for progressive working of electric products to be more efficient in this field.

A NOTE ON OPERATORS ON FINSLER MODULES

  • TAGHAVI, A.;JAFARZADEH, JAFARZADEH
    • Honam Mathematical Journal
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    • v.28 no.4
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    • pp.533-541
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    • 2006
  • let E be a Finsler modules over $C^*$-algebras. A with norm-map $\rho$ and L(E) set of all A-linear bonded operators on E. We show that the canonical homomorphism ${\phi}:L(E){\rightarrow}L(E_I)$ sending each operator T to its restriction $T|E_I$ is injective if and only if I is an essential ideal in the underlying $C^*$-algebra A. We also show that $T{\in}L(E)$ is a bounded below if and only if ${\mid}{\mid}x{\mid}{\mid}={\mid}{\mid}{\rho}{\prime}(x){\mid}{\mid}$ is complete, where ${\rho}{\prime}(x)={\rho}(Tx)$ for all $x{\in}E$. Also, we give a necessary and sufficient condition for the equivalence of the norms generated by the norm map.

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EXACTNESS OF IDEAL TRANSFORMS AND ANNIHILATORS OF TOP LOCAL COHOMOLOGY MODULES

  • BAHMANPOUR, KAMAL
    • Journal of the Korean Mathematical Society
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    • v.52 no.6
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    • pp.1253-1270
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    • 2015
  • Let (R, m) be a commutative Noetherian local domain, M a non-zero finitely generated R-module of dimension n > 0 and I be an ideal of R. In this paper it is shown that if $x_1,{\ldots },x_t$ ($1{\leq}t{\leq}n$) be a sub-set of a system of parameters for M, then the R-module $H^t_{(x_1,{\ldots },x_t)}$(R) is faithful, i.e., Ann $H^t_{(x_1,{\ldots },x_t)}$(R) = 0. Also, it is shown that, if $H^i_I$ (R) = 0 for all i > dim R - dim R/I, then the R-module $H^{dimR-dimR/I}_I(R)$ is faithful. These results provide some partially affirmative answers to the Lynch's conjecture in [10]. Moreover, for an ideal I of an arbitrary Noetherian ring R, we calculate the annihilator of the top local cohomology module $H^1_I(M)$, when $H^i_I(M)=0$ for all integers i > 1. Also, for such ideals we show that the finitely generated R-algebra $D_I(R)$ is a flat R-algebra.