• 대한수학회보
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• 제55권3호
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• pp.777-788
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• 2018

A simple poset is a poset whose linear discrepancy increases if any relation of the poset is removed. In this paper, we investigate more important properties of simple posets such as its width and height which help to construct concrete simple poset of linear discrepancy l. The simplicity of a poset is similar to the ld-irreducibility of a poset. Hence, we investigate which posets are both simple and ld-irreducible. Using these properties, we characterize n-posets of linear discrepancy n - k for k = 2, 3, and, lastly, we also characterize a poset of linear discrepancy 3 with simple posets and ld-irreducible posets.

• 대한수학회지
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• 제45권3호
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• pp.711-725
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• 2008

We give an explicit construction of Grobner-Shirshov pairs and monomial bases for finite-dimensional irreducible representations of the simple Lie algebra $sp_4$. We also identify the monomial basis consisting of the reduced monomials with a set of semistandard tableaux of a given shape, on which we give a colored oriented graph structure.

• 호남수학학술지
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• 제29권2호
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• pp.269-277
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• 2007

Let L := L(G) denote the classical modular Lie algebra of $E_6$-type over an algebraically closed field F of characteristic p > 5 associated with some simple and simply connected algebraic group G. After the prototypes of those for $E_8$-type in [4], we shall search for irreducible (=simple) L-modules in this paper.

• Journal of the Korean Data and Information Science Society
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• 제18권3호
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• pp.827-832
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• 2007

Several partial orders on integral partitions have been studied with many applications such as majorizations, capacities of quantum memory and embeddabilities of matrix algebras. In particular, the embeddability, stable embeddability and strong-stable embeddability problems arise for finite dimensional irreducible modules over a complex simple Lie algebra L. We find a sufficient condition for an L-module strong-stably embeds into another L-module using formal character theory.

• 대한수학회보
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• 제31권1호
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• pp.61-72
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• 1994

Every irreducible block-finite orthomodular lattice is simple [9] and every irreducible orthomodular alttice such that no proper p-ideal of L contains infinitely many commutators is simple [5]. Every finite (height) OML L which does not belong to the varitety generated by MO2 has one of the OML MO3, 2$^{3}$.2$^{2}$, D$_{16}$ OMLHOUSE as the homomorpyhic image of a subalgebra of L [3]. In this paper, we extend these results.s.

• 대한수학회논문집
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• 제12권4호
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• pp.1023-1032
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• 1997

This paper deals with certain conditions under which irreducibility of a 3-manifold is preserved under attaching a 2-handle along a simple closed curve (and then, if necessary, capping off a 2-sphere boundary component by a 3-ball).

• East Asian mathematical journal
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• 제14권2호
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• pp.259-268
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• 1998

In this paper, for a commutative ring R with an identity, considering the endomorphism ring $End_R$(M) of left R-module $_RM$ which is (quasi-)injective or (quasi-)projective, some discriminations of prime endomorphism were found as follows: each epimorphism with the irreducible(or simple) kernel on a (quasi-)injective module and each monomorphism with maximal image on a (quasi-)projective module are prime. It was shown that for a field F, any given square matrix in $Mat_{n{\times}n}$(F) with maximal image and irreducible kernel is a prime matrix, furthermore, any given matrix in $Mat_{n{\times}n}$(F) for any field F can be factored into a product of prime matrices.

• 충청수학회지
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• 제1권1호
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• pp.43-53
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• 1988

The main result of this paper is a characterization of almost projective modules over art in algebras by means of irreducible maps and almost split sequences. A module X is an almost projective module if and only if it has a presentation $0{\longrightarrow}L{\longrightarrow^{\alpha}}P{\longrightarrow}X{\longrightarrow}0$ with projective module P and irreducible maps ${\alpha}$. Let X be an injective almost projective non simple module and $0{\rightarrow}Dtr(x){\rightarrow}E{\rightarrow}X{\rightarrow}0$ be an almost split sequence. If $E=E_1{\oplus}E_2$ is a direct decomposition of indecomposable modules then ${\ell}(X)=3$.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.1-20
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• 2020

A simple but elegant result of Rival states that every sublattice L of a finite distributive lattice 𝒫 can be constructed from 𝒫 by removing a particular family 𝒥_L of its irreducible intervals. Applying this in the case that 𝒫 is a product of a finite set 𝒞 of chains, we get a one-to-one correspondence L ↦ 𝒟_𝒫(L) between the sublattices of 𝒫 and the preorders spanned by a canonical sublattice 𝒞^⋄ of 𝒫. We then show that L is a tight sublattice of the product of chains 𝒫 if and only if 𝒟_𝒫(L) is asymmetric. This yields a one-to-one correspondence between the tight sublattices of 𝒫 and the posets spanned by its poset J(𝒫) of non-zero join-irreducible elements. With this we recover and extend, among other classical results, the correspondence derived from results of Birkhoff and Dilworth, between the tight embeddings of a finite distributive lattice L into products of chains, and the chain decompositions of its poset J(L) of non-zero join-irreducible elements.

• 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.