• The Mathematical Education
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• v.12 no.2
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• pp.5-12
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• 1974

단위원을 가지는 하환환에 있어서의 Prime Spectrum에 관하여 다음 세가지 사실을 증명하였다. 1. X를 환 R의 prime spectrum, C(X)를 X에서 정의되는 실연적함수의 환, X를 C(X)의 maximal spectrum이라 하면 X는 C(X)의 prime spectrum의 부분공간으로서의 한 T-space로 된다. N을 환 R의 nilradical이라 하면, R/N이 regula 이면 X와 X는 위상동형이다. 2. f: R$\longrightarrow$R'을 ring homomorphism, P를 R의 한 Prime ideal, $R_{p}$, R'$_{p}$를 각각 S=R-P 및 f(S)에 관한 분수환(ring of fraction)이라 하고, k(P)를 local ring $R_{p}$의 residue' field라 할 때, R'의 prime spectrum의 부분공간인 $f^{*-1}$(P)는 k(P)(equation omitted)$_{R}$R'의 prime spectrum과 위상동형이다. 단 f*는 f*(Q)=$f^{-1}$(Q)로서 정의되는 함수 s*:Spec(R')$\longrightarrow$Spec(R)이다. 3. X를 환 S의 prime spectrum, N을 R의 nilradical이라 할 때, 다음 네가지 사실은 동치이다. (1) R/N 은 regular 이다. (2) X는 Zarski topology에 관하여 Hausdorff 공간이다. (3) X에서의 Zarski topology와 constructible topology와는 일치한다. (4) R의 임의의 원소 f에 대하여 f를 포함하지 않는 R의 prime ideal 전체의 집합 $X_{f}$는 Zarski topology에 관하여 개집합인 동시에 폐집합이다.폐집합이다....

• Proceedings of the Korean Information Science Society Conference
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• 2006.10d
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• pp.112-117
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• 2006

그리드 환경은 원격의 이질적인 자원들을 서로 공유하며 상호 접근이 가능하도록 하여 사용자의 작업을 처리할 수 있는 메커니즘을 제공한다. 이때 그리드에 참여하는 각 노드들은 그리드에 자유롭게 참여 및 탈퇴가 가능하다는 점에서 P2P(Peer-to-Peer) 네트워크 구조와 유사하다. 또한 그리드 정보 서비스의 배치(deployment)와 특정한 자원 검색 서비스의 측면을 고려할 때 P2P 구조는 그리드 환경에서 유용하게 활용 될 수 있다. 따라서 그리드를 설계함에 있어 기존의 방법과는 달리 P2P 형식으로 그리드를 구성하는 것은 시스템의 확장성과 이에 따른 효율성을 개선하는 중요한 요소가 된다. 본 논문에서는 P2P 형식의 그리드를 구성하는데 필요한 계층형 Ring 기반의 멤버쉽 프로토콜을 제안한다. 계층형 Ring 기반의 멤버쉽 프로토콜은 제한된 네트워크 연결만을 가지게 되므로 멤버쉽을 위한 통신 비용을 감소 시킬 수 있게 되며, 각 노드에서 유지해야 하는 멤버쉽 정보들이 지역적인 정보들만을 대상으로 하기 때문에 멤버쉽 정보 유지에 따른 관리 비용 또한 감소하게 되는 장점을 갖게 된다.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.629-633
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• 2003

We investigate in this paper rings containing a finitely generated p-injective maximal left ideal. We show that if R is a semiprime ring containing a finitely generated p-injective maximal left ideal, then R is a left p-injective ring. Using this result we are able to give a new characterization of von Neumann regular rings with nonzero socle.

• Korean Journal of Environmental Agriculture
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• v.30 no.3
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• pp.229-233
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• 2011

BACKGROUND: Soil acidification, which is known to be one of the reasons of forest decline, is associated with decreases in exchangeable Ca and increases in Al concentration, leading to low Ca/Al ratio in soil solution. As tree rings are datable archives of environmental changes, Ca/Al ratios of annual growth ring may show decreasing pattern in accordance with the progress of soil acidification. This study was conducted to investigate Ca/Al pattern of Pinus densiflora tree ring in an attempt to test its usefulness as an indicator of historical soil acidification. METHODS AND RESULTS: Three P. densiflora tree disks were collected from P. densiflora forests in Jeonnam province, and soil samples (0-10, 10-20, and 20-30 cm in depth) were also collected from the tree locations. Soils were analyzed for pH and exchangeable Ca and Al concentrations, and Ca/Al was calculated. Annual growth rings formed between 1969 and 2007 were separated and analyzed for Ca/Al. Soil Ca/Al was positively (P<0.01) correlated with soil pH, suggesting that soil acidification decreased Ca while increasing Al availability, lowering Ca/Al in soil solution. The Ca/Al of tree rings also showed a decreasing pattern from 18.2 to 5.5 during the period, and this seemed to reflect historical acidification of the soils. CONCLUSION(s): The relationship between soil pH and Ca/Al and the decreasing pattern of Ca/Al of tree ring suggest that Ca/Al of tree ring needs to be considered as a proxy of the progress of soil acidification in P. densiflora forest in southern Korea.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.255-260
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• 2006

Let $m$ and $k$ be any positive integers, let $\mathbb{Z}_k$ the ring of integers of modulo $k$, let $G_m(\mathbb{Z}_k)$ the group of all $m$ by $m$ nonsingular matrices over $\mathbb{Z}_k$ and let ${\phi}_m(k)$ the order of $G_m(\mathbb{Z}_k)$. In this paper, ${\phi}_m(k)$ can be computed by the following investigation: First, for any relatively prime positive integers $s$ and $t$, $G_m(\mathbb{Z}_{st})$ is isomorphic to $G_m(\mathbb{Z}_s){\times}G_m(\mathbb{Z}_t)$. Secondly, for any positive integer $n$ and any prime $p$, ${\phi}_m(p^n)=p^{m^2}{\cdot}{\phi}_m(p^{n-1})=p{^{2m}}^2{\cdot}{\phi}_m(p^{n-2})={\cdots}=p^{{(n-1)m}^2}{\cdot}{\phi}_m(p)$, and so ${\phi}_m(k)={\phi}_m(p_1^n1){\cdot}{\phi}_m(p_2^{n2}){\cdots}{\phi}_m(p_s^{ns})$ for the prime factorization of $k$, $k=p_1^{n1}{\cdot}p_2^{n2}{\cdots}p_s^{ns}$.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.285-297
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• 2008

For an endomorphism ${\alpha}$ of a ring R, the endomorphism ${\alpha}$ is called semicommutative if ab=0 implies $aR{\alpha}(b)$=0 for a ${\in}$ R. A ring R is called ${\alpha}$-semicommutative if there exists a semicommutative endomorphism ${\alpha}$ of R. In this paper, various results of semicommutative rings are extended to ${\alpha}$-semicommutative rings. In addition, we introduce the notion of an ${\alpha}$-skew power series Armendariz ring which is an extension of Armendariz property in a ring R by considering the polynomials in the skew power series ring $R[[x;\;{\alpha}]]$. We show that a number of interesting properties of a ring R transfer to its the skew power series ring $R[[x;\;{\alpha}]]$ and vice-versa such as the Baer property and the p.p.-property, when R is ${\alpha}$-skew power series Armendariz. Several known results relating to ${\alpha}$-rigid rings can be obtained as corollaries of our results.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.853-866
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• 2014

Constacyclic codes of length $p^s$ over $R=\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}+u^2\mathbb{F}_{p^m}$ are precisely the ideals of the ring $\frac{R[x]}{<x^{p^s}-1>}$. In this paper, we investigate constacyclic codes of length $p^s$ over R. The units of the ring R are of the forms ${\gamma}$, ${\alpha}+u{\beta}$, ${\alpha}+u{\beta}+u^2{\gamma}$ and ${\alpha}+u^2{\gamma}$, where ${\alpha}$, ${\beta}$ and ${\gamma}$ are nonzero elements of $\mathbb{F}_{p^m}$. We obtain the structures and Hamming distances of all (${\alpha}+u{\beta}$)-constacyclic codes and (${\alpha}+u{\beta}+u^2{\gamma}$)-constacyclic codes of length $p^s$ over R. Furthermore, we classify all cyclic codes of length $p^s$ over R, and by using the ring isomorphism we characterize ${\gamma}$-constacyclic codes of length $p^s$ over R.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.05a
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• pp.306-310
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• 2004

In this paper, we consider the Ring Loading Problem with integer demand splitting (RLP). The problem is given with a ring network, in which a required traffic requirement between each selected node pair must be routed on it. Each traffic requirement can be routed in both directions on the ring network while splitting each traffic requirement in two directions only by integer is allowed. The problem is to find an optimal routing of each traffic requirement which minimizes the capacity requirement. Here, the capacity requirement is defined as the maximum of traffic loads imposed on each link on the network. We formulate the problem as an integer program. By characterizing every extreme point solution to the LP relaxation of the formulation, we show that the optimal objective value of the LP relaxation is equal to p or p+0.5, where p is a nonnegative integer. We also show that the difference between the optimal objective value of RLP and that of the LP relaxation is at most 1. Therefore, we can verify that the optimal objective value of RLP is p+1 if that of the LP relaxation is p+0.5. On the other hand, we present a strengthened LP with size polynomially bounded by the input size, which provides enough information to determine if the optimal objective value of RLP is p or p+1.

• Journal of Integrative Natural Science
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• v.11 no.2
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• pp.107-112
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• 2018

p38 MAP kinase belongs to the Mitogen-activated protein (MAP) kinase family; a serine/threonine kinase. It plays an important role in intracellular signal transduction pathways. It is associated with the development and progression of various cancer types making it a crucial drug target. Present study involves the HQSAR analysis of recently reported imidazo[1,2-b]pyridazine derivatives as p38 MAP kinase antagonists. The model was generated with Atom (A), bond (B), chirality (Ch), and hydrogen (H) parameters and with different set of atom counts to improve the model. An acceptable HQSAR model ($q^2=0.522$, SDEP=0.479, NOC=5, $r^2=0.703$, SEE=0.378, BHL=97) was developed which exhibits good predictive ability. A contribution map for the most active compound (compound 17) illustrated that hydrogen and nitrogen atoms in the ring A and ring B, as well as nitrogen atom in ring C and the hydrogen atom in the ring D provided positive activity in inhibitory effect while, the least active compound (compound 05) possessed negative contribution to inhibitory effect. Hence, analysis of produced HQSAR model can provide insights in the designing potent and selective p38 MAP kinase antagonists.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1075-1082
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• 2018

Let R be a commutative ring, G be an Abelian group, and let RG be the group ring. We say that RG is a U-group ring if a is a unit in RG if and only if ${\epsilon}(a)$ is a unit in R. We show that RG is a U-group ring if and only if G is a p-group and $p{\in}J(R)$. We give some properties of U-group rings and investigate some properties of well known rings, such as Hermite rings and rings with stable range, in the presence of U-group rings.