• Title/Summary/Keyword: M&A Module

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ON NOETHERIAN PSEUDO-PRIME SPECTRUM OF A TOPOLOGICAL LE-MODULE

  • Anjan Kumar Bhuniya;Manas Kumbhakar
    • Communications of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.1-9
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    • 2023
  • An le-module M over a commutative ring R is a complete lattice ordered additive monoid (M, ⩽, +) having the greatest element e together with a module like action of R. This article characterizes the le-modules RM such that the pseudo-prime spectrum XM endowed with the Zariski topology is a Noetherian topological space. If the ring R is Noetherian and the pseudo-prime radical of every submodule elements of RM coincides with its Zariski radical, then XM is a Noetherian topological space. Also we prove that if R is Noetherian and for every submodule element n of M there is an ideal I of R such that V (n) = V (Ie), then the topological space XM is spectral.

FINITELY GENERATED gr-MULTIPLICATION MODULES

  • Park, Seungkook
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.4
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    • pp.717-723
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    • 2012
  • In this paper, we investigate when gr-multiplication modules are finitely generated and show that if M is a finitely generated gr-multiplication R-module then there is a lattice isomorphism between the lattice of all graded ideals I of R containing ann(M) and the lattice of all graded submodules of M.

ON THE CHAIN CONDITIONS OF A FAITHFUL ENDO-FLAT MODULE

  • Bae, Soon-Sook
    • Communications of the Korean Mathematical Society
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    • v.14 no.1
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    • pp.1-12
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    • 1999
  • The faithful bi-module \ulcornerM\ulcorner with its endomorphism ring End\ulcorner(M) such that M\ulcorner is flat (in other words, End\ulcorner(M)-flat, or endo-flat)and with a commutative ring R containing an identity has been studied in this paper. The chain conditions of a faithful endo-flat module \ulcornerM relative to those of the endomorphism ring End\ulcorner(M) having the zero annihilator of each non-zero endomorphism are studied.

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Knowledge Evolution based Machine-Tool in M2M Environment-Analysis of Ping Agent Based on FIPA-OS and Design of Dialogue Agent Module (M2M환경에서의 지식진화형 지능공작기계-FIPA-OS를 사용하는 Ping Agent 분석 및 Dialogue Agent 모듈설계)

  • Kim, Dong-Hun;Song, Jun-Yeop
    • 연구논문집
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    • s.34
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    • pp.113-119
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    • 2004
  • Recently, the conventional concept of a machine-tool in manufacturing systems is changing from the target of integration to the autonomous manufacturing device based on a knowledge evolution. Subsequently, a machine-tool has been the subject of a cooperation through an advanced environment where an open architecture controller, high speed network and internet technology are contained In the future, a machine-tool will be more improved in the form of a knowledge evolution based device. In order to develop the knowledge evolution based machine-tool, this paper proposes the structure of knowledge evolution and the scheme of a dialogue agent among agent-based modules such as a sensory module, a dialogue module, and an expert system. The dialogue agent has a role of interfacing with another machine for cooperation. To design of the dialogue agent module in M2M(Machine To Machine)environment, FIPA-OS and ping agent based on FIPA-OS are analyzed in this study. Through this, it is expected that the dialogue agent module can be more efficiently designed and the knowledge evolution based machine-tool can be hereafter more easily implemented.

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A Construction Theory of Arithmetic Operation Unit Systems over $GF(2^m)$ ($GF(2^m)$ 상의 산술연산기시스템 구성 이론)

  • 박춘명;김흥수
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.27 no.6
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    • pp.910-920
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    • 1990
  • This paper presents a method of constructing an Arithmetic Operation Unit Systems (A.O.U.S.) over Galois Field GF(2**m) for the purpose of the four arithmetical operation(addition, subtraction, multiplication and division between two elements in GF(2**mm). The proposed A.O.U.S. is constructed by following procedure. First of all, we obtained each four arithmetical operation algorithms for performing the four arithmetical operations using by mathematical properties over GF(2**m). Next, for the purpose of realizing the four arithmetical unit module (adder module, subtracter module, multiplier module and divider module), we constructed basic cells using the four arithmetical operation algorithms. Then, we realized the four Arithmetical Operation Unit Modules(A.O.U.M.) using basic cells and we constructd distributor modules for the purpose of merging A.O.U.M. with distributor modules. Finally, we constructed the A.O.U.S. over GF(2**m) by synthesizing A.O.U.M. with distributor modules. We prospect that we are able to construct an Arithmetic & Logical Operation Unit Systems (A.L.O.U.S.) if we will merge the proposed A.O.U.S. in this paper with Logical Operation Unit Systems (L.O.U.S.).

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THE CONNECTED SUBGRAPH OF THE TORSION GRAPH OF A MODULE

  • Ghalandarzadeh, Shaban;Rad, Parastoo Malakooti;Shirinkam, Sara
    • Journal of the Korean Mathematical Society
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    • v.49 no.5
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    • pp.1031-1051
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    • 2012
  • In this paper, we will investigate the concept of the torsion-graph of an R-module M, in which the set $T(M)^*$ makes up the vertices of the corresponding torsion graph, ${\Gamma}(M)$, with any two distinct vertices forming an edge if $[x:M][y:M]M=0$. We prove that, if ${\Gamma}(M)$ contains a cycle, then $gr({\Gamma}(M)){\leq}4$ and ${\Gamma}(M)$ has a connected induced subgraph ${\overline{\Gamma}}(M)$ with vertex set $\{m{\in}T(M)^*{\mid}Ann(m)M{\neq}0\}$ and diam$({\overline{\Gamma}}(M)){\leq}3$. Moreover, if M is a multiplication R-module, then ${\overline{\Gamma}}(M)$ is a maximal connected subgraph of ${\Gamma}(M)$. Also ${\overline{\Gamma}}(M)$ and ${\overline{\Gamma}}(S^{-1}M)$ are isomorphic graphs, where $S=R{\backslash}Z(M)$. Furthermore, we show that, if ${\overline{\Gamma}}(M)$ is uniquely complemented, then $S^{-1}M$ is a von Neumann regular module or ${\overline{\Gamma}}(M)$ is a star graph.

A GENERALIZATION OF THE ZERO-DIVISOR GRAPH FOR MODULES

  • Safaeeyan, Saeed;Baziar, Mohammad;Momtahan, Ehsan
    • Journal of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.87-98
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    • 2014
  • Let R be a commutative ring with identity and M an R-module. In this paper, we associate a graph to M, say ${\Gamma}(M)$, such that when M = R, ${\Gamma}(M)$ is exactly the classic zero-divisor graph. Many well-known results by D. F. Anderson and P. S. Livingston, in [5], and by D. F. Anderson and S. B. Mulay, in [6], have been generalized for ${\Gamma}(M)$ in the present article. We show that ${\Gamma}(M)$ is connected with $diam({\Gamma}(M)){\leq}3$. We also show that for a reduced module M with $Z(M)^*{\neq}M{\backslash}\{0\}$, $gr({\Gamma}(M))={\infty}$ if and only if ${\Gamma}(M)$ is a star graph. Furthermore, we show that for a finitely generated semisimple R-module M such that its homogeneous components are simple, $x,y{\in}M{\backslash}\{0\}$ are adjacent if and only if $xR{\cap}yR=(0)$. Among other things, it is also observed that ${\Gamma}(M)={\emptyset}$ if and only if M is uniform, ann(M) is a radical ideal, and $Z(M)^*{\neq}M{\backslash}\{0\}$, if and only if ann(M) is prime and $Z(M)^*{\neq}M{\backslash}\{0\}$.

w-INJECTIVE MODULES AND w-SEMI-HEREDITARY RINGS

  • Wang, Fanggui;Kim, Hwankoo
    • Journal of the Korean Mathematical Society
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    • v.51 no.3
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    • pp.509-525
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    • 2014
  • Let R be a commutative ring with identity. An R-module M is said to be w-projective if $Ext\frac{1}{R}$(M,N) is GV-torsion for any torsion-free w-module N. In this paper, we define a ring R to be w-semi-hereditary if every finite type ideal of R is w-projective. To characterize w-semi-hereditary rings, we introduce the concept of w-injective modules and study some basic properties of w-injective modules. Using these concepts, we show that R is w-semi-hereditary if and only if the total quotient ring T(R) of R is a von Neumann regular ring and $R_m$ is a valuation domain for any maximal w-ideal m of R. It is also shown that a connected ring R is w-semi-hereditary if and only if R is a Pr$\ddot{u}$fer v-multiplication domain.

GALOIS GROUPS OF MODULES AND INVERSE POLYNOMIAL MODULES

  • Park, Sang-Won;Jeong, Jin-Sun
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.2
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    • pp.225-231
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    • 2007
  • Given an injective envelope E of a left R-module M, there is an associative Galois group Gal$({\phi})$. Let R be a left noetherian ring and E be an injective envelope of M, then there is an injective envelope $E[x^{-1}]$ of an inverse polynomial module $M[x^{-1}]$ as a left R[x]-module and we can define an associative Galois group Gal$({\phi}[x^{-1}])$. In this paper we describe the relations between Gal$({\phi})$ and Gal$({\phi}[x^{-1}])$. Then we extend the Galois group of inverse polynomial module and can get Gal$({\phi}[x^{-s}])$, where S is a submonoid of $\mathbb{N}$ (the set of all natural numbers).

GALOIS GROUP OF GENERALIZED INVERSE POLYNOMIAL MODULES

  • Park, Sang-Won;Jeong, Jin-Sun
    • East Asian mathematical journal
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    • v.24 no.2
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    • pp.139-144
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    • 2008
  • Given an injective envelope E of a left R-module M, there is an associative Galois group Gal($\phi$). Let R be a left noetherian ring and E be an injective envelope of M, then there is an injective envelope E[$x^{-1}$] of an inverse polynomial module M[$x^{-1}$] as a left R[x]-module and we can define an associative Galois group Gal(${\phi}[x^{-1}]$). In this paper we extend the Galois group of inverse polynomial module and can get Gal(${\phi}[x^{-s}]$), where S is a submonoid of $\mathds{N}$ (the set of all natural numbers).

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