• 대한수학회지
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• 제39권4호
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• pp.611-620
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• 2002

The aim of the Paper is to Obtain information about the flat covers and minimal flat resolutions of Artinian modules over a Noetherian ring. Let R be a commutative Noetherian ring and let A be an Artinian R-module. We prove that the flat cover of a is of the form $\prod_{p\epsilonAtt_R(A)}T-p$, where $Tp$ is the completion of a free R$_{p}$-module. Also, we construct a minimal flat resolution for R/xR-module 0: $_AX$ from a given minimal flat resolution of A, when n is a non-unit and non-zero divisor of R such that A = $\chiA$. This result leads to a description of the structure of a minimal flat resolution for ${H^n}_{\underline{m}}(R)$, nth local cohomology module of R with respect to the ideal $\underline{m}$, over a local Cohen-Macaulay ring (R, $\underline{m}$) of dimension n.

• 대한수학회지
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• 제51권4호
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• pp.655-663
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• 2014

Let R be a ring with identity, X(R) the set of all nonzero, non-units of R and G(R) the group of all units of R. We show that for a matrix ring $M_n(D)$, $n{\geq}2$, if a, b are singular matrices of the same rank, then ${\mid}o_{\ell}(a){\mid}={\mid}o_{\ell}(b){\mid}$, where $o_{\ell}(a)$ and $o_{\ell}(b)$ are the orbits of a and b, respectively, under the left regular action. We also show that for a semisimple Artinian ring R such that $X(R){\neq}{\emptyset}$, $$R{{\sim_=}}{\oplus}^m_{i=1}M_n_i(D_i)$$, with $D_i$ infinite division rings of the same cardinalities or R is isomorphic to the ring of $2{\times}2$ matrices over a finite field if and only if ${\mid}o_{\ell}(x){\mid}={\mid}o_{\ell}(y){\mid}$ for all $x,y{\in}X(R)$.

• 대한수학회보
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• 제38권3호
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• pp.543-549
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• 2001

We show that R[X] is a Krull (Resp. factorial) ring if and only if R is a normal Krull (resp, factorial) ring with a finite number of minimal prime ideals if and only if R is a Krull (resp. factorial) ring with a finite number of minimal prime ideals and R(sub)M is an integral domain for every maximal ideal M of R. As a corollary, we have that if R[X] is a Krull (resp. factorial) ring and if D is a Krull (resp. factorial) overring of R, then D[X] is a Krull (resp. factorial) ring.

• 한국구조물진단유지관리공학회 논문집
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• 제18권6호
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• pp.50-59
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• 2014

본 논문에서는 경북 구미시 봉곡천에 최근 건설된 다기능어도를 대상으로 SAP2000으로 구조 해석하기 위한 변수를 R/C Slab, R/C+S/C Slab 및 지하이동통로 규격(가로${\times}$세로)을 $1m{\times}0.2m$, $1m{\times}0.4m$, $1m{\times}0.6m$와 유속 0.8m/s, 1.2m/s, 1.6m/s으로 구분하여 해석한 결과와 봉곡천 설계식을 비교하여 안정성을 검토하였다. 봉곡천의 설계식 보다 R/C+S/C Slab 타입이 지하이동통로 출구부는 휨모멘트와 최대응력은 각각 28~54%, 26~50%, 측벽은 24~47%, 17~31%, 상부슬래브인 경우도 10~27%, 4~20% 적게 나타났다. 따라서 최대응력과 휨모멘트가 R/C+S/C Slab 타입이 구조 안정성이 확보되는 것으로 나타났기 때문에 지하통로는 휨모멘트와 최대 응력이 27%, 25%, 측벽은 24%, 15% 상부슬래브는 14%, 10%의 보완이 요구되는 것으로 판단된다. 이러한 결과는 지하이동통로 규격이 봉곡천 규격과 동일한 $1m{\times}0.4m$일 때가 $1m{\times}0.2m$, $1m{\times}0.6m$ 보다 안정성이 가장 유리한 것으로 확인되었다. 또한 해석 및 분석 결과를 근거로 다기능어도 시공 시 기본 자료로 활용이 기대된다.

• 대한수학회지
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• 제48권6호
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• pp.1189-1201
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• 2011

Let R be a ring and M a right R-module, S = $End_R$(M). The module M is called almost principally small injective (or APS-injective for short) if, for any a ${\in}$ J(R), there exists an S-submodule $X_a$ of M such that $l_Mr_R$(a) = Ma $Ma{\bigoplus}X_a$ as left S-modules. If $R_R$ is a APS-injective module, then we call R a right APS-injective ring. We develop, in this paper, APS-injective rings as a generalization of PS-injective rings and AP-injective rings. Many examples of APS-injective rings are listed. We also extend some results on PS-injective rings and AP-injective rings to APS-injective rings.

• 대한수학회보
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• 제48권6호
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• pp.1125-1128
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• 2011

Let R be a commutative Noetherian ring, a an ideal of R, and M a minimax R-module. We prove that the local cohomology modules $H^j_a(M)$ are a-cominimax; that is, $Ext^i_R$(R/a, $H^j_a(M)$) is minimax for all i and j in the following cases: (a) dim R/a = 1; (b) cd(a) = 1, where cd is the cohomological dimension of a in R; (c) dim $R{\leq}2$. In these cases we also prove that the Bass numbers and the Betti numbers of $H^j_a(M)$ are finite.

• 미생물학회지
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• 제19권3호
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• pp.103-107
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• 1981

1 계면활성제의 농도가 증가하면 용해도와 최소억제농도는 일정하게 증가한다. 2 계연활성제에 결합되어 있는 지방산의 탄소수가 증가하면 용해도와 최소억제농도는 증가한다. 3 용해도와 최소억제농도와의 관계는 $S-S_0=R^{\prime}/R^{\prime\prime}\;(M-M_0)$로써, 본 실험에서 $R^{\prime}/R^{\prime\prime}$는 대략 2가 되었다.

• 한국정보디스플레이학회:학술대회논문집
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• 한국정보디스플레이학회 2002년도 International Meeting on Information Display
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• pp.325-328
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• 2002

We developed a high performance 2.2" active matrix OLED display for IMT-2000 mobile phone. Scan and Data driver circuits were integrated on the glass substrate, using low temperature poly-Si(LTPS) TFT CMOS technology. High efficiency EL materials were employed to the panel for low power consumption. Peak luminescence of the panel was higher than 250cd/$m^2$ with power consumption of 200mW.

• 대한수학회지
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• 제51권1호
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• pp.87-98
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• 2014

Let R be a commutative ring with identity and M an R-module. In this paper, we associate a graph to M, say ${\Gamma}(M)$, such that when M = R, ${\Gamma}(M)$ is exactly the classic zero-divisor graph. Many well-known results by D. F. Anderson and P. S. Livingston, in [5], and by D. F. Anderson and S. B. Mulay, in [6], have been generalized for ${\Gamma}(M)$ in the present article. We show that ${\Gamma}(M)$ is connected with $diam({\Gamma}(M)){\leq}3$. We also show that for a reduced module M with $Z(M)^*{\neq}M{\backslash}\{0\}$, $gr({\Gamma}(M))={\infty}$ if and only if ${\Gamma}(M)$ is a star graph. Furthermore, we show that for a finitely generated semisimple R-module M such that its homogeneous components are simple, $x,y{\in}M{\backslash}\{0\}$ are adjacent if and only if $xR{\cap}yR=(0)$. Among other things, it is also observed that ${\Gamma}(M)={\emptyset}$ if and only if M is uniform, ann(M) is a radical ideal, and $Z(M)^*{\neq}M{\backslash}\{0\}$, if and only if ann(M) is prime and $Z(M)^*{\neq}M{\backslash}\{0\}$.

• 대한수학회보
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• 제59권1호
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• pp.213-226
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• 2022

Let R be a ring and M an R-module. Then M is said to be regular w-flat provided that the natural homomorphism I ⊗_R M → R ⊗_R M is a w-monomorphism for any regular ideal I. We distinguish regular w-flat modules from regular flat modules and w-flat modules by idealization constructions. Then we give some characterizations of total quotient rings and Prüfer v-multiplication rings (PvMRs for short) utilizing the homological properties of regular w-flat modules.