• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.269-275
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• 1998

We find the Hibert functions of basic configurations in $P^n$. In particular we obtain the minimal generators of the ideal of a weak-k-configuration in $P^n$.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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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.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.547-551
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• 1998

We give some examples of extremal minimal free reso-lutions of Gorenstein ideals of codimension 4.

• Korean Journal of Mathematics
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• v.4 no.2
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• pp.101-115
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• 1996

In this paper, we will show that the minimal number of generators of any four dimensional, faithful, $\mathcal{B}$(Schur algebra of size 4)-module is two. This result can be applied to classify the isomorphism classes of the class {$\mathcal{B}{\ltimes}N^2{\mid}N$ is a faithful, $\mathcal{B}$-module with $dim_k(N)=4$}.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.1017-1023
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• 2010

We prove that a maximal ideal M of D[x] has two generators and is of the form where p is an irreducible element in a PID D having infinitely many nonassociate irreducible elements and q(x) is an irreducible non-constant polynomial in D[x]. Moreover, we find how minimal generators of maximal ideals of a polynomial ring D[x] over a DVR D consist of and how many generators those maximal ideals have.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.553-561
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• 2007

In this paper we propose the concept of fuzzy basis of fuzzy submachine, which is the generalized form of crisp basis of submachine, and we extend the system of generators and free subset to fuzzy forms, from which we prove that minimal system of fuzzy generators, maximally free fuzzy subset, and fuzzy basis are equivalent forms.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.249-261
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• 1997

We find a necessary and sufficient condition for a $\kappa$-confi-guration $\mathbb{X}$ in $\mathbb{P}^2$ to be in generic position. We obtain the number and degrees of minimal generators of some Gorenstein ideals of codimension 3 and so obtain their minimal free resolution s of these ideals.

• East Asian mathematical journal
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• v.38 no.3
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• pp.347-355
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• 2022

For a nondegenerate projective variety, it is a classical problem to study its defining equations with respect to a given embedding. In this paper, we precisely determine minimal sets of generators of the defining ideals of some curves of maximal regularity in ℙ⁵.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.149-155
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• 1998

In this paper, we construct the minimal set of generators which generate the subgroup T of the Weyl group of Kac-Moody algebra.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.563-569
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• 2014

We investigate a minimal set of generators of a homogeneous ideal of a curve of degree d on a linearly normal smooth surface scroll W in $P^r$ whose arithmetic genus is maximal among curves of degree d on W.