• 호남수학학술지
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• 제36권2호
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• pp.387-398
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• 2014

In this paper, we give a structure theorem for a class of Gorenstein ideal of grade 4 which is the sum of an almost complete intersection of grade 3 and a Gorenstein ideal of grade 3 geometrically linked by a regular sequence. We also present the Hilbert function of a Gorenstein ideal of grade 4 induced by a Gorenstein matrix f.

• 대한수학회보
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• 제54권1호
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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.

• 호남수학학술지
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• 제36권3호
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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.

• 대한수학회논문집
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• 제23권4호
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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.

• 대한수학회보
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• 제37권4호
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• pp.829-841
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• 2000

We classify complete intersections I of grade 3 in a regular local ring (R, M) by the number of minimal generators of a minimal prime ideal P over I. Here P is either a complete intersection or a Gorenstein ideal which is not a compete intersection.

• 대한수학회지
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• 제54권5호
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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 $I_i{\cap}J_i$.