• Korean Journal of Mathematics
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• 제8권1호
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• pp.19-26
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• 2000

In this paper, it is shown that if R is a commutative ring with identity and there exists a multiplicatively closed subset S of R such that $S{\cap}Z(R/(I_1I_2{{\cdots}I_n))={\emptyset}$ and $I_1R_s,I_2R_s{\cdots},I_nR_s$ are pairwise comaximal, then $I_1I_2{\cdots}I_n=I_1{\cap}I_2{\cap}{\cdots}{\cap}I_n={\cap}^n_{i=1}(I_i\;:_R\;I_1{\cdots}I_{i-1}I_{i+1}{\cdots}I_n)$.

• 정보관리학회지
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• 제6권1호
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• pp.3-14
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• 1989

본 연구는 학술 잡지의 발달 과정과 그 특징, 연구 논문 편수의 증가와 학회의 발달 과를 고찰하므로서 우리나라 학자들의 논문 발표의 주된 수단이 무엇인지, 학술 정보의 생 산과 축적 수단으로서 학술 잡지의 기능을 밝히고 도서관 정보 봉사를 설계하거나 개선함에 있어 올바른 방향 설정에 도움이 될 객관적 근거를 마련하는데 그 목적이 있다.

• 대한수학회보
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• 제22권2호
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• pp.121-126
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• 1985

D.K. Harrison [5] has shown that if R and S are fields of characteristic different from 2, then two Witt rings W(R) and W(S) are isomorphic if and only if W(R)/I(R)$^{3}$ and W(S)/I(S)$^{3}$ are isomorphic where I(R) and I(S) denote the fundamental ideals of W(R) and W(S) respectively. In [1], J.K. Arason and A. Pfister proved a corresponding result when the characteristics of R and S are 2, and, in [9], K.I. Mandelberg proved the result when R and S are commutative semi-local rings having 2 a unit. In this paper, we prove the result when R and S are 2-fold full rings. Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is nondegenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$ (V, R) induced by B is an isomorphism), and with a quadratic mapping .phi.:V.rarw.R such that B(x,y)=(.phi.(x+y)-.phi.(x)-.phi.(y))/2 and .phi.(rx)= $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U(R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$, .., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2, we reserve the notation [ $a_{11}$, $a_{22}$] for the space.the space.e.e.e.

• 대한수학회지
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• 제48권1호
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• pp.105-115
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• 2011

Let f be a function which assigns a positive integer f(v) to each vertex v $\in$ V (G), let r, s and t be non-negative integers. An f-coloring of G is an edge-coloring of G such that each vertex v $\in$ V (G) has at most f(v) incident edges colored with the same color. The minimum number of colors needed to f-color G is called the f-chromatic index of G and denoted by ${\chi}'_f$(G). An [r, s, t; f]-coloring of a graph G is a mapping c from V(G) $\bigcup$ E(G) to the color set C = {0, 1, $\ldots$; k - 1} such that |c($v_i$) - c($v_j$ )| $\geq$ r for every two adjacent vertices $v_i$ and $v_j$, |c($e_i$ - c($e_j$)| $\geq$ s and ${\alpha}(v_i)$ $\leq$ f($v_i$) for all $v_i$ $\in$ V (G), ${\alpha}$ $\in$ C where ${\alpha}(v_i)$ denotes the number of ${\alpha}$-edges incident with the vertex $v_i$ and $e_i$, $e_j$ are edges which are incident with $v_i$ but colored with different colors, |c($e_i$)-c($v_j$)| $\geq$ t for all pairs of incident vertices and edges. The minimum k such that G has an [r, s, t; f]-coloring with k colors is defined as the [r, s, t; f]-chromatic number and denoted by ${\chi}_{r,s,t;f}$ (G). In this paper, we present some general bounds for [r, s, t; f]-coloring firstly. After that, we obtain some important properties under the restriction min{r, s, t} = 0 or min{r, s, t} = 1. Finally, we present some problems for further research.

• 대한수학회논문집
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• 제37권2호
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• pp.337-345
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• 2022

Let R ⊆ T be an extension of a commutative ring and S ⊆ R a multiplicative subset. We say that (R, T) is an S-accr (a commutative ring R is said to be S-accr if every ascending chain of residuals of the form (I : B) ⊆ (I : B²) ⊆ (I : B³) ⊆ ⋯ is S-stationary, where I is an ideal of R and B is a finitely generated ideal of R) pair if every ring A with R ⊆ A ⊆ T satisfies S-accr. Using this concept, we give an S-version of several different known results.

• 대한수학회지
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• 제39권1호
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• pp.127-135
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• 2002

Let I be an ideal in a Gorenstein local ring A with the maximal ideal m. Then we say that I is an equimultiple good ideal in A, if I contains a reduction Q = ( $a_1$, $a_2$,ㆍㆍㆍ, $a_{s}$ ) generated by s elements in A and G(I) =(equation omitted)$_{n 0}$ $I^{n}$ / $I^{n＋1}$ of I is a Gorenstein ring with a(G(I)) = 1 - s, where s = h $t_{A}$ I and a(G(I)) denotes the a-invariant of G(I). Let $X_{A}$$^{s}$ denote the set of equimultiple good ideals I in A with h $t_{A}$ I = s, R(I) = A [It] be the Rees algebra of I, and $K_{R(I)}$ denote the canonical module of R(I). Let a I such that $I^{n＋l}$ = a $I^{n}$ for some n$\geq$0 and $\mu$$_{A}$(I)$\geq$2, where $\mu$$_{A}$(I) denotes the number of elements in a minimal system of generators of I. Assume that A/I is a Cohen-Macaulay ring. We show that the following conditions are equivalent. (1) $K_{R(I)}$(equation omitted)R(I)＋as graded R(I)-modules. (2) $I^2$ = aI and aA : I$\in$ $X^1$$_{A}$._{A}$./.

• 정보관리학회지
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• 제6권1호
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• pp.15-36
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• 1989

마이크로 컴퓨터의 급속한 성장에 따라 그 이용 범위 또한 넓어지게 되었다. 본고에 서는 이러한 마이크로 컴퓨터를 이용해 원자력 정책 자료 검색 시스템을 설계하였다.

• 대한수학회보
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• 제39권4호
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• pp.653-663
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• 2002

We introduce and investigate the concepts of ($(T_i,T_j)$-fuzzy $\alpha-(r.s)$-semiopen $\alpha-(r.s)$-semiclosed) sets and fuzzy pairwise $\alpha-(r.s)$-semicontinuous mappings in smooth bitopological spaces.

• 대한수학회지
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• 제51권3호
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• pp.463-472
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• 2014

Let R be a ring with identity 1, I(R) be the set of all nonunit idempotents in R and $S_{\ell}$(R) (resp. $S_r$(R)) be the set of all left (resp. right) semicentral idempotents in R. In this paper, the following are investigated: (1) $e{\in}S_{\ell}(R)$ (resp. $e{\in}S_r(R)$) if and only if re=ere (resp. er=ere) for all nilpotent elements $r{\in}R$ if and only if $fe{\in}I(R)$ (resp. $ef{\in}I(R)$) for all $f{\in}I(R)$ if and only if fe=efe (resp. ef=efe) for all $f{\in}I(R)$ if and only if fe=efe (resp. ef=efe) for all $f{\in}I(R)$ which are isomorphic to e if and only if $(fe)^n=(efe)^n$ (resp. $(ef)^n=(efe)^n$) for all $f{\in}I(R)$ which are isomorphic to e where n is some positive integer; (2) For a ring R having a complete set of centrally primitive idempotents, every nonzero left (resp. right) semicentral idempotent is a finite sum of orthogonal left (resp. right) semicentral primitive idempotents, and eRe has also a complete set of primitive idempotents for any $0{\neq}e{\in}S_{\ell}(R)$ (resp. 0$0{\neq}e{\in}S_r(R)$).

• Journal of Plant Biology
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• 제29권1호
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• pp.53-65
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• 1986

The montane forests of Ulreung Island, Korea, were investigated by the ZM school method. By comparing the montane forests of this island with those of Korean Peninsula and of Japan, a new order, F a g e t a l i a m u l t i n e r v i s, a new alliance, F a l g i o n m u l t i n e r v i s, a new association, H e p a t i c o-F a g e t u m m u l t i n e r v i s and Rhododendron brachycarpum-Pinus parviflora community were recognized. The H e p a t i c o - F a g e t u m m u l t i n e r v i s was further subdivided into four subassociations; Subass. of Sasa kurilensis, Subass. of Rumohra standishii, Subass. of Rhododendron brachycarpum and Subass. of typicum. Each community was described in terms of floristic, structural and environmental features.