• Kyungpook Mathematical Journal
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• 제55권4호
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• pp.871-883
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• 2015

This paper is devoted to study the divisorial submodules. We get some equivalent conditions for a submodule to be a divisorial submodule. Also we get equivalent conditions for $(N{\cap}L)^{-1}$ to be a ring, where N, L are submodules of a module M.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 ITC-CSCC -1
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• pp.318-321
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• 2000

This paper propose the method of constructing the highly efficiency adder and multiplier systems over finite fie2, degree of uk terms, therefore we decrease k into m-1 degree using irreducible primitive polynomial. We propose two method of control signal generation for perform above decrease process. One method is the combinational logic expression and the other method is universal signal generation. The proposed method of constructing the highly adder/multiplier systems is as following. First of all, we obtain algorithms for addition and multiplication arithmetic operation based on the mathematical properties over finite fields, next we construct basic cell of A-cell and M-cell using T-gate and modP cyclic gate. Finally we construct adder module and multiplier module over finite fields after synthesize ${\alpha}$$\^$k/ generation module and control signal CSt generation module with A-cell and M-cell. Then, we propose the future research and prospects.

• 호남수학학술지
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• 제32권4호
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• pp.739-746
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• 2010

In this short paper, we show that properties of an ideal I of a ring R are related to those of the homogeneous ideal I(+)IM of a ring R(+)M.

• 호남수학학술지
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• 제31권3호
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• pp.429-436
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• 2009

In this short paper, we prove some new properties on homogeneous ideals and primary ideals of R(+)M.

• 호남수학학술지
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• 제36권2호
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• pp.339-344
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• 2014

In this paper, we give some properties on projective modules, locally cyclic projective modules and the ideal ${\tau}(M)$.

• 대한수학회보
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• 제52권4호
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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).

• 대한수학회보
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• 제59권6호
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• pp.1387-1408
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• 2022

Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N :_R M)∩S = ∅ to be weakly S-prime if there exists s ∈ S such that whenever a ∈ R and m ∈ M with 0 ≠ am ∈ N, then either sa ∈ (N :_R M) or sm ∈ N. Many properties, examples and characterizations of weakly S-prime submodules are introduced, especially in multiplication modules. Moreover, we investigate the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations. Finally, we define two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are weakly S-prime.

• 대한전자공학회논문지
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• 제27권6호
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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.).

• 전기전자학회논문지
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• 제25권1호
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• pp.88-94
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• 2021

현재 사용되고 있는 RSA, ECC와 같은 공개키 암호화 기법은 소인수분해와 같은 현재의 컴퓨터로 계산이 오래 걸리는 수학적 문제를 암호화에 사용했다. 그러나 양자컴퓨터가 상용화된다면 Shor Algorithm에 의해 기존의 암호화 시스템은 쉽게 깨질 수 있다. 그로 인해 Quantum-resistant 한 암호화 알고리즘의 도입이 필요해졌고, 그중 하나로 Lattice-based Cryptography가 제안되고 있다. 이 암호화 알고리즘은 Polynomial Ring에서 연산이 행해지고, 그중 Polynomial Multiplication이 가장 큰 연산 시간을 차지한다. 그러므로 다항식 곱셈 계산을 빠르게 하는 하드웨어 모듈이 필요하고, 그중 Finite Field에서 연산 되는 FFT인 Number Theoretic Transform을 이용해서 다항식 곱셈을 계산하는 8-point NTT-based Polynomial Multiplier 모듈을 설계하고 시뮬레이션했다. HDL을 사용하여 로직검증을 수행하였고, Hspice를 사용하여 트랜지스터 수준에서 제안된 설계가 지연시간과 전력소모에서 얼마나 개선되는지를 비교 분석하였다. 제안된 설계에서 평균 지연속도 30%의 개선과 8% 이상의 전력소모 감소 효과를 볼 수 있었다.

• 대한수학회보
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• 제38권4호
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• pp.727-733
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• 2001

Let A be a commutative ring with nonzero identity and let M be an A-module. In this note we show that if $x = x_1, ..., x_n\; and\; y = y_1, ..., y_n$ both M-cosequence such that $Hx^T = y^T\; for\; some\; n\times n$ lower triangular matrix H over A, then the map $\beta_H : \;Ann_M(y_1,..., y_n)\;\rightarrow Ann_M(x_1,..., x_n)$ induced by multiplication by ｜H｜ is surjective.