• Honam Mathematical Journal
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• v.29 no.2
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• pp.119-192
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• 2007

A very important Hopf algebra is the graded Hopf algebra Symm of symmetric functions. It can be characterized as the unique graded positive selfdual Hopf algebra with orthonormal graded distinguished basis and just one primitive element from the distinguished basis. This result is due to Andrei Zelevinsky. A noncommutative graded Hopf algebra of this type cannot exist. But there is a most important positive graded Hopf algebra with distinguished basis that is noncommutative and that is twisted selfdual, the Malvenuto-Poirier-Reutenauer Hopf algebra of permutations. Thus the question arises whether there is a corresponding uniqueness theorem for MPR. This prepreprint records initial investigations in this direction and proves that uniquenees holds up to and including the degree 4 which has rank 24.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.333-339
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• 2009

In this manuscript, we introduce the concept of an atomic subset of the hyper BCK-algebra and study its properties. Also, we give a characterization of the atomic hyper BCK-algebra and show that there are exactly (up to isomorphism) n atomic hyper BCK-algebras H with |H| = n for any natural number n.

• Honam Mathematical Journal
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• v.17 no.1
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• pp.7-14
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• 1995

The purpose of this study is to construct the structure of the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$, which conforms to Stellmacher's [4] Pushing Up. The main idea of this paper comes from Stellmacher's [4] Pushing Up. Stelhnacher considered Pushing Up under a finite p-group. This paper, however, considers Pushing Up under the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$. In this paper, $O_p(G)$ in [4] is Q=exp(q), where q=nilrad(g) and a Sylow p-subgroup S in [7] is S=exp(s), where $s=q{\oplus}\{\(\array{0&*\\0&0}\){\mid}*{\in}\mathbb{F}\}$. Showing the properties of the connected Lie group and the subgroups of the connected Lie group with relations between a connected Lie group and its Lie algebras under the exponential map, this paper constructs the subgroup series C_z(G)

• Journal of the Korean Society for Railway
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• v.12 no.2
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• pp.267-275
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• 2009

Max-plus algebra is a nonlinear system comprised of two operations, maximization (max) and addition (Plus), which are corresponding to the addition and the multiplication in conventional algebra, respectively. This methodology is applicable to many discrete event systems containing the state transition with the maximization and addition operation. Timetable with connection is one of such systems. We present the method based on max-plus algebra, which can make up timetable considering transfer and analyse its stability and robustness. In this study, it will be shown how to make up the timetable of the urban train and analyse its stability using Max-Plus algebra.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.385-397
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• 2022

Let (M, [ , ]) be a finite dimensional Malcev algebra over an algebraically closed field 𝔽 of characteristic 0. We first prove that, (M, [ , ]) (with [M, M] ≠ 0) is simple if and only if ind(M) = 1 (i.e., M admits a unique (up to a scalar multiple) invariant scalar product). Further, we characterize the form of skew-symmetric biderivations on simple Malcev algebras. In particular, we prove that the simple seven dimensional non-Lie Malcev algebra has no nontrivial skew-symmetric biderivation.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.747-762
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• 2023

ω-left-symmetric algebras contain left-symmetric algebras as a subclass and the commutator defines an ω-Lie algebra. In this paper, we classify ω-left-symmetric algebras in dimension 3 up to an isomorphism based on the classification of ω-Lie algebras and the technique of Lie algebras.

• The Mathematical Education
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• v.44 no.3 s.110
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• pp.337-360
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• 2005

In this paper we develop textbook 'Modem Algebra' for training mathematics teacher of secondary schools. In order to understand mathematics teacher's viewpoint about desirable textbook 'Modem Algebra' we created a Questionnaire related with curriculum and textbook for training mathematics teacher of secondary schools. We analyze the result of the questionnaire along with recent studies on teacher education and come up with basic principles of developing textbook 'Modern Algebra'. The first version of 'Modern Algebra for Mathematics Teachers' that we have developed based on our study can be found in website 'www.teacheredu.co.kr'.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.345-367
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• 2016

The concept of derivations of BCI-algebras was first introduced by Jun and Xin. In this paper, we introduce the notions of (l, r)-derivations, (r, l)-derivations and derivations of UP-algebras and investigate some related properties. In addition, we define two subsets $Ker_d(A)$ and $Fix_d(A)$ for some derivation d of a UP-algebra A, and we consider some properties of these as well.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.2
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• pp.115-142
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• 2018

This research analyzed domestic researches on early algebra education which are published in six major mathematics education journals in Korea. The purpose of this work is to grasp trends of early algebra education in Korea and to draw up future tasks. From 2000 to 2017, 89 papers which are related to early algebra education published in 6 journals. The 89 papers were categorized by research period, academic journals, research topics, and research subjects. As a result, the number of researches on early algebra education in Korea has increased since 2000. Although early algebra education belongs to the field of elementary mathematics education, lots of papers were published in other math education journals than in the math education journals for elementary school mathematics. Most research focused on proportional reasoning across the algebraic content area. The majority of the research subjects were students, especially upper-grade students of elementary school. Based on the results of this study, some implications for early algebra education in Korea were suggested.

• Annals of Fuzzy Mathematics and Informatics
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• v.16 no.3
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• pp.317-331
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• 2018

This paper aims to extend the notion of hesitant fuzzy sets on UP-algebras to hesitant fuzzy soft sets over UP-algebras by merging the notions of hesitant fuzzy sets and soft sets. Further, we discuss the notions of hesitant fuzzy soft strongly UP-ideals, hesitant fuzzy soft UP-ideals, hesitant fuzzy soft UP-filters, and hesitant fuzzy soft UP-subalgebras of UP-algebras, and provide some properties.