• Title, Summary, Keyword: multiplication module

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THE w-WEAK GLOBAL DIMENSION OF COMMUTATIVE RINGS

  • WANG, FANGGUI;QIAO, LEI
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.4
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    • pp.1327-1338
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    • 2015
  • In this paper, we introduce and study the w-weak global dimension w-w.gl.dim(R) of a commutative ring R. As an application, it is shown that an integral domain R is a $Pr\ddot{u}fer$ v-multiplication domain if and only if w-w.gl.dim(R) ${\leq}1$. We also show that there is a large class of domains in which Hilbert's syzygy Theorem for the w-weak global dimension does not hold. Namely, we prove that if R is an integral domain (but not a field) for which the polynomial ring R[x] is w-coherent, then w-w.gl.dim(R[x]) = w-w.gl.dim(R).

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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A low-power VLSI architecture of 4D TCM decoder for ADSL (ADSL용 4D TCM Decoder 저전력 구조 설계 연구)

  • 이금형;김재석
    • Proceedings of the IEEK Conference
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    • pp.871-874
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    • 1999
  • We propose a low complexity M-D(multidimensional) TCM decoder VLSI architecture for ADSL System. We use the shared subset decoder module by modifying the whole decoding procedure. We reduce power consumption by using the MSA (modulo set area) operation, which removes multiplication in 4D metric calculation. Also the proposed TCM decoder reduces chip area. It can be adopted in high-speed xDSL system.

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ON AGE RINGS AND AM MODULES WITH RELATED CONCEPTS

  • Cho, Yong-Uk
    • East Asian mathematical journal
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    • v.18 no.2
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    • pp.245-259
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    • 2002
  • In this paper, all rings or (left)near-rings R are associative, and for near-ring R, all R-groups are right R action and all modules are right R-modules. First, we begin with the study of rings in which all the additive endomorphisms or only the left multiplication endomorphisms are generated by ring endomorphisms and their properties. This study was motivated by the work on the Sullivan's Problem [14]. Next, for any right R-module M, we will introduce AM modules and investigate their basic properties. Finally, for any nearring R, we will also introduce MR-groups and study some of their properties.

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On Graded Quasi-Prime Submodules

  • AL-ZOUBI, KHALDOUN;ABU-DAWWAS, RASHID
    • Kyungpook Mathematical Journal
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    • v.55 no.2
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    • pp.259-266
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    • 2015
  • Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded quasi-prime submodules and give some basic results about graded quasi-prime submodules of graded modules. Special attention has been paid, when graded modules are graded multiplication, to find extra properties of these submodules. Furthermore, a topology related to graded quasi-prime submodules is introduced.

Module-theoretic Characterizations of Strongly t-linked Extensions

  • Kim, Hwankoo;Kwon, Tae In
    • Kyungpook Mathematical Journal
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    • v.53 no.1
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    • pp.25-35
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    • 2013
  • In this paper, we introduce and study the concept of "strongly $t$-linked extensions", which is a stronger version of $t$-linked extensions of integral domains. We show that for an extension of Pr$\ddot{u}$fer $v$-multiplication domains, this concept is equivalent to that of "$w$-faithfully flat".

A Study on the Exploratory Learning in Groups Method in Mathematics Education (수학 교과에서의 집단탐구식 수업 방법에 관한 고찰)

  • Hwang, Hye-Jeong
    • Journal of Educational Research in Mathematics
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    • v.12 no.1
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    • pp.1-16
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    • 2002
  • The 7th Curriculum emphasizes that in mathematics classes, mathematical concepts be understood and mathematical problems be solved through student's own exploratory activities including the use of data, manipulatives, andtechnological devices. Following the main idea of the Seventh Mathematics Curriculum, this paper dealt with instructional methods applied suitably and effectively in mathematics classes, and focused on the 'exploratory learning in groups' method in mathematics education. For this purpose, this paper reviewed and summarized theories related to general pedagogy and of mathematics education. Based on the results, it investigated appropriate instructional methods in mathematics education. In particular, this paper focused on studying the exploratory learning method while investigating its properties and understand- ing the relationship between the 'exploratory learning in groups' method and the discussion-centered method. Finally, in order to show the usefulness of the exploratory learning method, this paper developed an example of a teaching module using the exploratory learning method in addition to discussion and lecture-centered methods by the use of manipulatives. The main goal of the module was to make students understand the principle of multiplication of integers.

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A Design of Modular Multiplier Based on Improved Multi-Precision Carry Save Adder (개선된 다정도 CSA에 기반한 모듈라 곱셈기 설계)

  • Kim, Dae-Young;Lee, Jun-Yong
    • Journal of KIISE:Computer Systems and Theory
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    • v.33 no.4
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    • pp.223-230
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    • 2006
  • The method of implementing a modular multiplier for Montgomery multiplication by using an adder depends on a selected adder. When using a CPA, there is a carry propagation problem. When using a CSA, it needs an additional calculation for a final result. The Multiplier using a Multi-precision CSA can solve both problems simultaneously by combining a CSA and a CPA. This paper presents an improved MP-CSA which reduces hardware resources and operation time by changing a MP-CSA's carry chain structure. Consequently, the proposed multiplier is more suitable for the module of long bit multiplication and exponentiation using a modular multiplier repeatedly.

Design of High-Speed Parallel Multiplier on Finite Fields GF(3m) (유한체 GF(3m)상의 고속 병렬 곱셈기의 설계)

  • Seong, Hyeon-Kyeong
    • Journal of the Korea Society of Computer and Information
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    • v.20 no.2
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    • pp.1-10
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    • 2015
  • In this paper, we propose a new multiplication algorithm for primitive polynomial with all 1 of coefficient in case that m is odd and even on finite fields $GF(3^m)$, and design the multiplier with parallel input-output module structure using the presented multiplication algorithm. The proposed multiplier is designed $(m+1)^2$ same basic cells. Since the basic cells have no a latch circuit, the multiplicative circuit is very simple and is short the delay time $T_A+T_X$ per cell unit. The proposed multiplier is easy to extend the circuit with large m having regularity and modularity by cell array, and is suitable to the implementation of VLSI circuit.