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SOME CONDITIONS FOR COMAXIMALITY OF IDEALS

  • Ahn, Sung Hun
    • 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 $I_1I_2{\cdots}I_n=I_1{\cap}I_2{\cap}{\cdots}{\cap}I_n={\cap}^n_{i=1}(I_i\;:_R\;I_1{\cdots}I_{i-1}I_{i+1}{\cdots}I_n)$.

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제한효소 Sma I, Xma I, AVa I, Nae I의 DNA절단반응에 있어서 Hpa II methylation의 억제효과 (Inhibition of Sma I, Ava I, Nae I, and Xma I endonuclease activities by the methylation of DNA with Hpa II methylase)

  • 최우성;강선철;서정선;유욱준
    • 미생물학회지
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    • 제24권2호
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    • pp.86-90
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    • 1986
  • The DNA methylated by Hpa II methylase was not cleaved by Sma, I, Ava I and Nae I endonucleases. This experimental data could be interpreted as strong evidences that Sma I, Ava I and Nae I methylases which yet to be isolated would methylate on the inmost cytosine nucleotide within their hexameric recognition sequences. The facts that Sma I, Ava I and Nae I endonucleases can not cleave the DNA methylated by Hpa II methylase are the valuable informations for protecting DNAs upon cleavage reactions by Sma I, Ava I and NAe I endonucleases especially for cDNA insertion experiments into vector DNAs using Sma I, Ava I and Nae I oligonucleotide linkers. In the case of Xma I endonuclease, partially cleaved DNA fragments were observed although the reaction rate was greatly decreased. This result implies that the methylation site of Xma I methylase which yet to be isolated would not be the same as that of Hpa II methylase in Xma I sequence.

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EQUIMULTIPLE GOOD IDEALS WITH HEIGHT 1

  • Kim, Mee-Kyoung
    • 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}$._{A}$./.

COLOCALIZATION OF LOCAL HOMOLOGY MODULES

  • Rezaei, Shahram
    • 대한수학회보
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    • 제57권1호
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    • pp.167-177
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    • 2020
  • Let I be an ideal of Noetherian local ring (R, m) and M an artinian R-module. In this paper, we study colocalization of local homology modules. In fact we give Colocal-global Principle for the artinianness and minimaxness of local homology modules, which is a dual case of Local-global Principle for the finiteness of local cohomology modules. We define the representation dimension rI (M) of M and the artinianness dimension aI (M) of M relative to I by rI (M) = inf{i ∈ ℕ0 : HIi (M) is not representable}, and aI (M) = inf{i ∈ ℕ0 : HIi (M) is not artinian} and we will prove that i) aI (M) = rI (M) = inf{rIR𝖕 (𝖕M) : 𝖕 ∈ Spec(R)} ≥ inf{aIR𝖕 (𝖕M) : 𝖕 ∈ Spec(R)}, ii) inf{i ∈ ℕ0 : HIi (M) is not minimax} = inf{rIR𝖕 (𝖕M) : 𝖕 ∈ Spec(R) ∖ {𝔪}}. Also, we define the upper representation dimension RI (M) of M relative to I by RI (M) = sup{i ∈ ℕ0 : HIi (M) is not representable}, and we will show that i) sup{i ∈ ℕ0 : HIi (M) ≠ 0} = sup{i ∈ ℕ0 : HIi (M) is not artinian} = sup{RIR𝖕 (𝖕M) : 𝖕 ∈ Spec(R)}, ii) sup{i ∈ ℕ0 : HIi (M) is not finitely generated} = sup{i ∈ ℕ0 : HIi (M) is not minimax} = sup{RIR𝖕 (𝖕M) : 𝖕 ∈ Spec(R) ∖ {𝔪}}.

ON DIRECT SUMS IN BOUNDED BCK-ALGEBRAS

  • HUANG YISHENG
    • 대한수학회논문집
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    • 제20권2호
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    • pp.221-229
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    • 2005
  • In this paper we consider the decompositions of subdirect sums and direct sums in bounded BCK-algebras. The main results are as follows. Given a bounded BCK-algebra X, if X can be decomposed as the subdirect sum $\bar{\bigoplus}_{i{\in}I}A_i$ of a nonzero ideal family $\{A_i\;{\mid}\;i{\in}I\}$ of X, then I is finite, every $A_i$ is bounded, and X is embeddable in the direct sum $\bar{\bigoplus}_{i{\in}I}A_i$ ; if X is with condition (S), then it can be decomposed as the subdirect sum $\bar{\bigoplus}_{i{\in}I}A_i$ if and only if it can be decomposed as the direct sum $\bar{\bigoplus}_{i{\in}I}A_i$ ; if X can be decomposed as the direct sum $\bar{\bigoplus}_{i{\in}I}A_i$, then it is isomorphic to the direct product $\prod_{i{\in}I}A_i$.

SELF-ADJOINT INTERPOLATION FOR OPERATORS IN TRIDIAGONAL ALGEBRAS

  • Kang, Joo-Ho;Jo, Young-Soo
    • 대한수학회보
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    • 제39권3호
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    • pp.423-430
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    • 2002
  • Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_{}i$ = $Y_{i}$ for i/ = 1,2,…, n. In this article, we obtained the following : Let X = ($x_{i\sigma(i)}$ and Y = ($y_{ij}$ be operators in B(H) such that $X_{i\sigma(i)}\neq\;0$ for all i. Then the following statements are equivalent. (1) There exists an operator A in Alg L such that AX = Y, every E in L reduces A and A is a self-adjoint operator. (2) sup ${\frac{\parallel{\sum^n}_{i=1}E_iYf_i\parallel}{\parallel{\sum^n}_{i=1}E_iXf_i\parallel}n\;\epsilon\;N,E_i\;\epsilon\;L and f_i\;\epsilon\;H}$ < $\infty$ and $x_{i,\sigma(i)}y_{i,\sigma(i)}$ is real for all i = 1,2, ....

PCR-RFLP를 이용한 국내 분포 씨스트선충 4종의 동정 (Identification of Four Cyst Nematodes using PCR-RFLP in Korea)

  • 고형래;강헌일;박은형;김은화;이재국
    • 한국유기농업학회지
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    • 제27권3호
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    • pp.353-363
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    • 2019
  • To identify four cyst nematodes (Heterodera schachtii, H. trifolii, H. glycines, H. sojae) that are economically important plant-parasitic nematodes in Korea, restriction fragment length polymorphism (RFLP) by 8 endonucleases (PstI, VspI, AlwI, RsaI, MvaI, EcoRI, Eco72I, Hinf I) was performed based on sequence difference of mitochondrial DNA cytochrome c oxidase subunit I (COI) gene. As a result, species-specific DNA band patterns by RsaI endonuclease were observed in H. schachtii. The specific patterns was in H. trifolii by 3 endonucleases (VspI, AlwI, Hinf I), and was in H. glycines by Hinf I. While, H. sojae was not digested by 4 endonuclease (VspI, AlwI, RsaI, Hinf I). This study showed that four cyst nematodes could be distinguished using RFLP by 4 endonucleases (RsaI, VspI, AlwI, Hinf I) based on the sequence difference of COI gene.

P-I-OPEN MAPPINGS, P-I-CONTINUOUS MAPPINGS AND P-I-IRRESOLUTE MAPPINGS

  • Kim, Ji-Yoon;Kim, Chang-Su
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제16권4호
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    • pp.383-404
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    • 2009
  • The notions of P-I-open (closed) mappings, P-I-continuous mappings, P-I-neighborhoods, P-I-irresolute mappings and I-irresolute mappings are introduced. Relations between P-I-open (closed) mappings and I-open (closed) mappings are given. Characterizations of P-I-open (closed) mappings are provided. Relations between a P-I-continuous mapping and an I-continuous mapping are discussed, and characterizations of a P-I-continuous mapping are considered. Conditions for a mapping to be an I-irresolute mapping (resp. P-I-irresolute mapping) are provided.

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AN ASSOCIATED SEQUENCE OF IDEALS OF AN INCREASING SEQUENCE OF RINGS

  • Ali, Benhissi;Abdelamir, Dabbabi
    • 대한수학회보
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    • 제59권6호
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    • pp.1349-1357
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    • 2022
  • Let 𝒜 = (An)n≥0 be an increasing sequence of rings. We say that 𝓘 = (In)n≥0 is an associated sequence of ideals of 𝒜 if I0 = A0 and for each n ≥ 1, In is an ideal of An contained in In+1. We define the polynomial ring and the power series ring as follows: $I[X]\, = \,\{\, f \,=\, {\sum}_{i=0}^{n}a_iX^i\,{\in}\,A[X]\,:\,n\,{\in}\,\mathbb{N},\,a_i\,{\in}\,I_i \,\}$ and $I[[X]]\, = \,\{\, f \,=\, {\sum}_{i=0}^{+{\infty}}a_iX^i\,{\in}\,A[[X]]\,:\,a_i\,{\in}\,I_i \,\}$. In this paper we study the Noetherian and the SFT properties of these rings and their consequences.

I.T.I. Hollow Screw IMPLANT를 이용한 부분적 치아결손환자의 치험예 : 술전평가와 외과적술식

  • 김홍기
    • 대한치과의사협회지
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    • 제29권6호통권265호
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    • pp.463-465
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    • 1991
  • I.T.I. Hollow Screw Implant는 새로운 I.T.I. Bonefit의 槪念의 일부를 이루었으며, 從來의 I.T.I. IMPLANT의 10년 以上의 臨床經驗에 기초하고 있다. I.T.I. Implant의 特徵은 몇가지 있으나, 그 중에서도 特記할 만한 것은 1回法의 外科術式이라고 할 수 있다. 本論文에서는 I.T.I. Hollow Screw Implant를 사용한 部分的齒牙欠損患者의 治療에 대한 術前評價와 外科術式에 대하여 論하고저 한다. 植立된 111개 Implant중 110개가 合倂症을 나타내지 않고 Tissue-Integration을 達成했으며, 그 밖의 1개는 失敗했다. 이러한 結果는 1回法인 I.T.I. Hollow Screw Implant가 Tissue-Integration으로서 成功率이 높은 것을 証明하고 있다.

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