• 대한수학회보
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• 제47권5호
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• pp.1053-1066
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• 2010

In this paper, several properties of endomorphism rings of modules are investigated. A multiplication module M over a commutative ring R induces a commutative ring $M^*$ of endomorphisms of M and hence the relation between the prime (maximal) submodules of M and the prime (maximal) ideals of $M^*$ can be found. In particular, two classes of ideals of $M^*$ are discussed in this paper: one is of the form $G_{M^*}\;(M,\;N)\;=\;\{f\;{\in}\;M^*\;|\;f(M)\;{\subseteq}\;N\}$ and the other is of the form $G_{M^*}\;(N,\;0)\;=\;\{f\;{\in}\;M^*\;|\;f(N)\;=\;0\}$ for a submodule N of M.

• Kyungpook Mathematical Journal
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• 제50권1호
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• pp.101-107
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• 2010

A module M is said to satisfy the $EC_{11}$ condition if every ec-submodule of M has a complement which is a direct summand. We show that for a multiplication module over a commutative ring the $EC_{11}$ and P-extending conditions are equivalent. It is shown that the $EC_{11}$ property is not inherited by direct summands. Moreover, we prove that if M is an $EC_{11}$-module where SocM is an ec-submodule, then it is a direct sum of a module with essential socle and a module with zero socle. An example is given to show that the reverse of the last result does not hold.

• 대한수학회보
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• 제56권2호
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• pp.505-514
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• 2019

Let R be a commutative ring with identity and M be a unitary R-module. A submodule N of M is called a dense submodule if $Hom_R(M/N,\;E_R(M))=0$, where $E_R(M)$ is the injective hull of M. The R-module M is said to be monoform if any nonzero submodule of M is a dense submodule. In this paper, among the other results, it is shown that any kind of the following module is monoform. (1) The prime R-module M such that for any nonzero submodule N of M, $Ann_R(M/N){\neq}Ann_R(M)$. (2) Strongly prime R-module. (3) Faithful multiplication module over an integral domain.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1998년도 추계종합학술대회 논문집
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• pp.1025-1028
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• 1998

Hardware to implement the parallelized Floating-point rounding algorithm is described. For parallelized additions, we propose an addition module which has carry selection logic to generate two results accoring to the input valuse. A multiplication module for parallelized multiplications is also proposed to generate Sum and Carry bits as intermediate results. Since these modules process data in IEEE standard Floatingpoint double precision format, they are designed for 53-bit significands including hidden bits. Multiplication module is designed with a Booth multiplier and an array multiplier.

• 융합신호처리학회논문지
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• 제2권3호
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• pp.102-109
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• 2001

본 논문에서는 GF($P^{m}$ )상에서의 새로운 승산 알고리듬과 승산기 구성법을 나타내었다. 유한체 상에서의 두 원소에 대한 승산공식을 유도하였고 유도된 수식에 의해 승산기를 구성하였다. 적용예로 GF(3) 승산 모듈과 덧셈 모듈을 전류 모드 CMOS 기법을 적용하여 구현하였다. 이러한 모듈을 기본 모듈로 사용하여 GF(3$^{m}$ )승산기를 설계하였고 SPICE를 통하여 검증하였다. 제시된 승산기는 규칙적인 셀 구조를 사용하였고 단순히 규칙적인 내부 결선으로 구성된다. 따라서, 유한체 상에서 차수가 m 차로 증가하는 승산에 대해서도 간단히 확장이 가능하다.

• 대한수학회논문집
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• 제15권3호
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• pp.493-498
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• 2000

In this paper we find some properties of distinguished prime submodules of modules and prove theorems about the dimension of modules.

• 대한수학회보
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• 제59권5호
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• pp.1289-1304
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• 2022

In this note, we show that a strongly 𝜙-ring R is a 𝜙-PvMR if and only if any 𝜙-torsion-free R-module is 𝜙-w-flat, if and only if any GV-torsion-free divisible R-module is nonnil-absolutely w-pure, if and only if any GV-torsion-free h-divisible R-module is nonnil-absolutely w-pure, if and only if any finitely generated nonnil ideal of R is w-projective.

• Kyungpook Mathematical Journal
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• 제58권3호
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• pp.463-472
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• 2018

A Q-module is a module in which every nonzero submodule of M is a finite product of primary submodules of M. This paper is devoted to study some properties of Dedekind modules and Q-modules.

• Journal of information and communication convergence engineering
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• 제9권4호
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• pp.435-440
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• 2011

This paper propose the method of constructing the highly efficiency adder and multiplier systems over finite fields. The addition arithmetic operation over finite field is simple comparatively because that addition arithmetic operation is analyzed by each digit modP summation independently. But in case of multiplication arithmetic operation, we generate maximum k=2m-2 degree of ${\alpha}^k$ terms, therefore we decrease k into m-1 degree using irreducible primitive polynomial. We propose two method of control signal generation for the purpose of performing 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 synthesizing ${\alpha}^k$ generation module and control signal CSt generation module with A-cell and M-cell. Next, we constructing the arithmetic operation unit over finite fields. Then, we propose the future research and prospects.

• 대한수학회지
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• 제53권5호
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• pp.1167-1182
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• 2016

Let M be an R-module, where R is a commutative ring with identity 1 and let G(V,E) be a graph. In this paper, we study the graphs associated with modules over commutative rings. We associate three simple graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ to M called full annihilating, semi-annihilating and star-annihilating graph. When M is finite over R, we investigate metric dimensions in $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$. We show that M over R is finite if and only if the metric dimension of the graph $ann_f({\Gamma}(M_R))$ is finite. We further show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if M is a prime-multiplication-like R-module. We investigate the case when M is a free R-module, where R is an integral domain and show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if $$M{\sim_=}R$$. Finally, we characterize all the non-simple weakly virtually divisible modules M for which Ann(M) is a prime ideal and Soc(M) = 0.