• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.269-276
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• 2015

We investigate the Hopf algebra conjugation, ${\chi}$, of the mod 2 Steenrod algebra, $\mathcal{A}_2$, in terms of the Hopf algebra conjugation, ${\chi}^{\prime}$, of the mod 2 Leibniz-Hopf algebra. We also investigate the fixed points of $\mathcal{A}_2$ under ${\chi}$ and their relationship to the invariants under ${\chi}^{\prime}$.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.303-325
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• 2023

In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Maurer-Cartan elements are relative Rota-Baxter systems. This allows us to define a cohomology theory associated with a relative Rota-Baxter system. Finally, we study formal deformations and extendibility of finite order deformations of a relative Rota-Baxter system in terms of the cohomology theory.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1265-1279
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• 2017

In order to study the structure of arbitrary split Leibniz triple systems, we introduce the class of split Leibniz triple systems as the natural extension of the class of split Lie triple systems and split Leibniz algebras. By developing techniques of connections of roots for this kind of triple systems, we show that any of such Leibniz triple systems T with a symmetric root system is of the form $T=U+{\sum}_{[j]{\in}{\Lambda}^1/{\sim}}I_{[j]}$ with U a subspace of $T_0$ and any $I_{[j]}$ a well described ideal of T, satisfying $\{I_{[j]},T,I_{[k]}\}=\{I_{[j]},I_{[k]},T\}=\{T,I_{[j]},I_{[k]}\}=0 \text{ if }[j]{\neq}[k]$.

• Communications of Mathematical Education
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• v.26 no.4
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• pp.351-362
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• 2012

Until the 1950s, linear algebra was considered only as one of abstract and advanced mathematics subject among in graduate mathematics courses, mainly dealing with module in algebra. Since the 1960s, it has been a main subject in undergraduate mathematics education because matrices has been used all over. In Korea, it was considered as a course only for mathematics major students until 1980s. However, now it is a subject for all undergraduate students including natural science, engineering, social science since 1990s. In this paper, we investigate the early history of linear algebra and its development from a historical perspective and mathematicians who made contributions. Secondly, we explain why linear algebra became so popular in college mathematics education in the late 20th century. Contributions of Chinese and H. Grassmann will be extensively examined with many newly discovered facts.