• 대한수학회논문집
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• 제38권4호
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• pp.1001-1017
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• 2023

Let R be a commutative graded ring with nonzero identity and n a positive integer. Our principal aim in this paper is to introduce and study the notions of graded n-irreducible and strongly graded n-irreducible ideals which are generalizations of n-irreducible and strongly n-irreducible ideals to the context of graded rings, respectively. A proper graded ideal I of R is called graded n-irreducible (respectively, strongly graded n-irreducible) if for each graded ideals I₁, . . . , I_n+1 of R, I = I₁ ∩ · · · ∩ I_n+1 (respectively, I₁ ∩ · · · ∩ I_n+1 ⊆ I ) implies that there are n of the I_i 's whose intersection is I (respectively, whose intersection is in I). In order to give a graded study to this notions, we give the graded version of several other results, some of them are well known. Finally, as a special result, we give an example of a graded n-irreducible ideal which is not an n-irreducible ideal and an example of a graded ideal which is graded n-irreducible, but not graded (n - 1)-irreducible.

• 대한수학회보
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• 제42권1호
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• pp.121-131
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• 2005

This paper is motivated by the results in [6]. We study some properties of strongly irreducible submodules of a module. In fact, our objective is to investigate strongly irreducible modules and to examine in particular when sub modules of a module are strongly irreducible. For example, we show that prime submodules of a multiplication module are strongly irreducible, and a characterization is given of a multiplication module over a Noetherian ring which contain a non-prime strongly irreducible submodule.

• Korean Journal of Mathematics
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• 제19권3호
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• pp.263-272
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• 2011

In the paper [1], an explicit correspondence between certain cubic irreducible polynomials over $\mathbb{F}_q$ and cubic irreducible polynomials of special type over $\mathbb{F}_{q^2}$ was established. In this paper, we show that we can mimic such a correspondence for quintic polynomials. Our transformations are rather constructive so that it can be used to generate irreducible polynomials in one of the finite fields, by using certain irreducible polynomials given in the other field.

• 대한수학회논문집
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• 제36권1호
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• pp.189-196
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• 2021

Using ld-irreducible posets, we can easily characterize posets with respect to linear discrepancy. However, it is difficult to have the list of all the irreducible posets with respect to a given linear discrepancy. In this paper, we investigate some properties of disconnected posets and connected posets with respect to linear discrepancy, respectively and then we find various relationships between ld-irreducibily and connectedness. From these results, we suggest some methods to construct ld-irreducible posets.

• 호남수학학술지
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• 제28권3호
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• pp.327-332
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• 2006

Prime elements and ${\bigwedge}$-irreducible elements are introduced, and related properties are investigated.

• 한국수학사학회지
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• 제18권1호
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• pp.75-84
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• 2005

본 논문은 군표현에 관한 역사적 배경을 알아보고, 유한군의 기약지표에 대한 어떤 조건하에서 그 군이 자명하지 않는 아벨 정규부분군을 가짐에 대한 성질들과 기약지표들의 적에 대한 성질을 증명한다.

• 호남수학학술지
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• 제33권3호
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• pp.355-366
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• 2011

In this paper we investigate criteria that for an irreducible monic quadratic polynomial f(x) ${\in}$ $\mathbb{Q}$[x], $f{\circ}g$ is reducible over $\mathbb{Q}$ for an irreducible polynomial g(x) ${\in}$ $\mathbb{Q}$[x]. Odoni intrigued the discussion about an explicit form of irreducible polynomials f(x) such that $f{\cric}f$ is reducible. We construct a system of infitely many such polynomials.

• 대한수학회보
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• 제40권2호
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• pp.177-182
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• 2003

A metacyclic group is a group that has a cyclic normal subgroup with cyclic quotient. We characterize finite metacyclic groups that have faithful irreducible representations over a given field.

• 한국수학사학회지
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• 제11권2호
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• pp.83-90
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• 1998

Observing that for any compact space X, the minimal basically disconnected cover ${\bigwedge}Λ_X$ : ${\bigwedge}Λ_X{\leftrightarro}$ is ${\sigma}Z^#$-irreducible, we will show that the projective objects in the category of compact spaces and ${\sigma}Z^#$-irreducible maps are precisely basically disconnected spaces.

• 전자공학회논문지SC
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• 제38권1호
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• pp.27-34
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• 2001

[ $GF(2^m)$ ]의 기약 3항식인 $x^m+x+1$을 이용한 승산기 알고리즘은 Mastrovito에 의해 제안되었다. 본 논문에서는 기약 3항식 $x^m+x+1$에서 1$GF(2^m)$상의 원시 기약 3 항식을 전개하여 회로를 간략화 하였으며, 제안된 승산기 설계는 규칙적이며 모듈러 구조, 그리고 간단한 제어신호를 요하기 때문에 VLSI 실현이 용이하다고 사료된다.