• Title, Summary, Keyword: multiplication module

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SEMIPRIME SUBMODULES OF GRADED MULTIPLICATION MODULES

  • Lee, Sang-Cheol;Varmazyar, Rezvan
    • Journal of the Korean Mathematical Society
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    • v.49 no.2
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    • pp.435-447
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    • 2012
  • Let G be a group. Let R be a G-graded commutative ring with identity and M be a G-graded multiplication module over R. A proper graded submodule Q of M is semiprime if whenever $I^nK{\subseteq}Q$, where $I{\subseteq}h(R)$, n is a positive integer, and $K{\subseteq}h(M)$, then $IK{\subseteq}Q$. We characterize semiprime submodules of M. For example, we show that a proper graded submodule Q of M is semiprime if and only if grad$(Q){\cap}h(M)=Q+{\cap}h(M)$. Furthermore if M is finitely generated then we prove that every proper graded submodule of M is contained in a graded semiprime submodule of M. A proper graded submodule Q of M is said to be almost semiprime if (grad(Q)$\cap$h(M))n(grad$(0_M){\cap}h(M)$) = (Q$\cap$h(M))n(grad$(0_M){\cap}Q{\cap}h(M)$). Let K, Q be graded submodules of M. If K and Q are almost semiprime in M such that Q + K $\neq$ M and $Q{\cap}K{\subseteq}M_g$ for all $g{\in}G$, then we prove that Q + K is almost semiprime in M.

Pattern recognition of multiplication environment of lactic acid bacteria in curd yogurt prepared by household fermentation system (가정용 호상 요구르트 발효기를 이용한 유산균 증식환경의 패턴 인식)

  • Shin, Seung-Hun;Choi, Sie-Young;Lee, Eun-Ju;Kwak, Bong-Soon;Kim, Jong-Boo
    • Journal of Sensor Science and Technology
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    • v.17 no.2
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    • pp.151-155
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    • 2008
  • In this paper, it was investigated that the pattern recognition of multiplication environment of lactic acid bacteria in the process of curd yogurt preparation using household fermentation system, which was manufactured by combining incubator with sensor module, data processing circuit and computer. It will be sufficiently applicable to determine the maximum ratio of the amount of air to mixed milk for preparation of high quality yogurt.

TWISTED HOPF COMODULE ALGEBRAS (2)

  • Park, Jun Seok
    • Journal of the Chungcheong Mathematical Society
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    • v.14 no.1
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    • pp.85-103
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    • 2001
  • Suppose that Hand K are paired Hopf algebras and that A is an H - K - bicomodule algebra with multiplication which is a left H-comodule map and is a right K-comodule map. We define a new twisted algebra, $A^{\tau}$ and define $M^{\tau}$ for $M{\in}M_A^K$. We find an equivalent condition for $M^{\tau}{\in}M_{A^{\tau}}^K$. We show that the above defined twisted multiplication is the special case of Beattie's twist multiplication. We show that if K is commutative, then A is an H-module algebra and show that if $H^*$ is cocommutative then the construction of smash product appears as a special case of the new twist product.

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Bit-level 1-dimensional systolic modular multiplication (비트 레벨 일차원 시스톨릭 모듈러 승산)

  • 최성욱;우종호
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.33B no.9
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    • pp.62-69
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    • 1996
  • In this paper, the bit-level 1-dimensional systolic array for modular multiplication is designed. First of all, the parallel algorithm and data dependence graph from walter's method based on montgomery algorithm suitable for array design for modular multiplication is derived. By the systematic procedure for systolic array design, four 1-dimensional systolic arrays are obtained and then are evaluated by various criteria. As it is modified the array which is derived form [0,1] projection direction by adding a control logic and it is serialized the communication paths of data A, optimal 1-dimensional systolic array is designed. It has constant I/O channels for expansile module and it is easy for fault tolerance due to unidirectional paths. It is suitable for RSA cryptosystem which deals iwth the large size and many consecutive message blocks.

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Pointwise Projective Modules and Some Related Modules

  • NAOUM-ADIL, GHASAN;JAMIL-ZEANA, ZAKI
    • Kyungpook Mathematical Journal
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    • v.43 no.4
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    • pp.471-480
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    • 2003
  • Let $\mathcal{R}$ be a commutative ring with 1, and Let M be a (left) R-module. M is said to be pointwise projective if for each epimorphism ${\alpha}:\mathcal{A}{\rightarrow}\mathcal{B}$, where A and $\mathcal{B}$ are any $\mathcal{R}$-modules, and for each homomorphism ${\beta}:\mathcal{M}{\rightarrow}\mathcal{B}$, then for every $m{\in}\mathcal{M}$, there exists a homomorphism ${\varphi}:\mathcal{M}{\rightarrow}\mathcal{A}$, which may depend on m, such that ${\alpha}{\circ}{\varphi}(m)={\beta}(m)$. Our mean concern in this paper is to study the relations between pointwise projectivemodules with cancellation modules and its geeralization.

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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.

ON ω-LOCAL MODULES AND Rad-SUPPLEMENTED MODULES

  • Buyukasik, Engin;Tribak, Rachid
    • Journal of the Korean Mathematical Society
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    • v.51 no.5
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    • pp.971-985
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    • 2014
  • All modules considered in this note are over associative commutative rings with an identity element. We show that a ${\omega}$-local module M is Rad-supplemented if and only if M/P(M) is a local module, where P(M) is the sum of all radical submodules of M. We prove that ${\omega}$-local nonsmall submodules of a cyclic Rad-supplemented module are again Rad-supplemented. It is shown that commutative Noetherian rings over which every w-local Rad-supplemented module is supplemented are Artinian. We also prove that if a finitely generated Rad-supplemented module is cyclic or multiplication, then it is amply Rad-supplemented. We conclude the paper with a characterization of finitely generated amply Rad-supplemented left modules over any ring (not necessarily commutative).

A Study on Constructing Highly Adder/multiplier Systems over Galois Felds

  • Park, Chun-Myoung
    • Proceedings of the IEEK Conference
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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.

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