• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.99-124
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• 2017

The structure theorems [3, 6, 21] for the classes of perfect ideals of grade 3 have been generalized to the structure theorems for the classes of perfect ideals linked to almost complete intersections of grade 3 by a regular sequence [15]. In this paper we obtain structure theorems for two classes of Gorenstein ideals of grade 4 expressed as the sum of a perfect ideal of grade 3 (except a Gorenstein ideal of grade 3) and an almost complete intersection of grade 3 which are geometrically linked by a regular sequence.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.487-497
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• 2008

Buchsbaum and Eisenbud showed that every Gorenstein ideal of grade 3 is generated by the submaximal order pfaffians of an alternating matrix. In this paper, we describe a method for constructing a class of type 3, grade 3, perfect ideals which are not Gorenstein. We also prove that they are algebraically linked to an even type grade 3 almost complete intersection.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.605-622
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• 2014

We provide a minimal free resolution for a class of Gorenstein ideal of grade 4 which is the sum of an almost complete intersection J of grade 3 and a perfect ideal I of grade 3 with type 2 and ${\lambda}(I)$ > 0 geometrically linked by a regular sequence, where I is generated by odd elements.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.715-736
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• 2012

Brown provided a structure theorem for a class of perfect ideals of grade 3 with type ${\lambda}$ > 0. We introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4 in a Noetherian local ring. We construct a class of perfect ideals I of grade 3 with type 2 defined by a certain skew-symmetrizable matrix. We present the Hilbert function of the standard $k$-algebras R/I, where R is the polynomial ring $R=k[v_0,v_1,{\ldots},v_m]$ over a field $k$ with indeterminates $v_i$ and deg $v_i=1$.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.279-287
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• 2012

Let $k$ be a field containing the field $\mathbb{Q}$ of rational numbers and let $R=k[x_{ij}{\mid}1{\leq}i{\leq}m,\;1{\leq}j{\leq}n]$ be the polynomial ring over a field $k$ with indeterminates $x_{ij}$. Let $I_t(X)$ be the determinantal ideal generated by the $t$-minors of an $m{\times}n$ matrix $X=(x_{ij})$. Eagon and Hochster proved that $I_t(X)$ is a perfect ideal of grade $(m-t+1)(n-t+1)$. We give a structure theorem for a class of determinantal ideals of grade 3. This gives us a characterization that $I_t(X)$ has grade 3 if and only if $n=m+2$ and $I_t(X)$ has the minimal free resolution $\mathbb{F}$ such that the second dierential map of $\mathbb{F}$ is a matrix defined by complete matrices of grade $n+2$.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1379-1410
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• 2017

Kang and Ko introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4. Let $R=k[w_0,\;w_1,\;w_2,\;{\ldots},\;w_m]$ be the polynomial ring over an algebraically closed field k with indetermiantes $w_l$ and deg $w_l=1$, and $I_i$ a homogeneous perfect ideal of grade 3 with type $t_i$ defined by a skew-symmetrizable matrix $G_i(1{\leq}t_i{\leq}4)$. We show that for m = 2 the Hilbert function of the zero dimensional standard k-algebra $R/I_i$ is determined by CI-sequences and a Gorenstein sequence. As an application of this result we show that for i = 1, 2, 3 and for m = 3 a Gorenstein sequence $h(R/H_i)=(1,\;4,\;h_2,\;{\ldots},\;h_s)$ is unimodal, where $H_i$ is the sum of homogeneous perfect ideals $I_i$ and $J_i$ which are geometrically linked by a homogeneous regular sequence z in $I_i{\cap}J_i$.

• The Korean Nurse
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• v.29 no.3
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• pp.25-35
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• 1990

It is a fact that there are recent increasing trends or incidence of the colorectal carcinoma among other colorectal diseases. In such trend, the early detection remain to be most important by the air contrast barium enema and total colonofiberscopy. There are several ways to prepare the colon for barium enema and colonofiberscopy which include several agents. The mechanical cleansing have been used most frequently since Brown's method was adapted to be most perfect for colon deansing. The ideal laxatives and enema solutions were limited to adequate dose, it's effectiveness, patient's diet and bowel habit, minimal side effect, low cost and simple to perform. In order to compare the effectiveness of various cleansing solutions, six experimental methods were formed as shown; 1. normal saline enema, 2. castor oil with normal saline enema, 3. castor oil with soap suds enema, 4. magnesium citrate with normal saline, 5. magnesium citrate with soap suds enema and 6. ingestion of Golyetly solution. The authors have compared and determined the degree of cleanness by an experienced endoscopist. The total number of patients was 247, age distribution was $43{\pm}15$ years old, and sex distribution was 133 males and 114 females. The grade I and II represented no difficulties at performing the colonofiberscopy, but grade ill and N had some difficulties, even unable to perform the colonofiberscopy. The effectiveness the cleansing agents, represented with grade I and II was 95.9% (47/49) in method 6, 93.2%(54/58) in method 2, 83.3%(30/33) in method 3, 70.0%(28/10) in method 5, 66.7%(16/24) in method i, and 45.7%(18/40) in method 4. Method 2 and 6 were the most effective in normal bowel habit patients. In constipated patients, method 6 was the most effective and all method except method 11 were effective in diarrhea patients. The degrees of less mucosal irritation by various bowel cleansing method were in the order of method 6(100%), 1(100%), 5(74%), 2(69%). In subjective symptoms and cleansing groups, abdominal distension, pain, nausea and vomiting were complained, and that's subject symptoms were in the order of method 3(88.9%), 6 (79.6%), 1(75%), 5(72.5%), 2(72.4%), 4(67.5%). In conclusion, we believe that the Golytely of the mechanical cleansing solution for colonofiberscopy was the most effective, but others depended on the patient's condition und bowel habit.