• Journal of the Korean Institute of Intelligent Systems
• /
• v.13 no.2
• /
• pp.243-246
• /
• 2003

In this paper we define a weak positive implicative hyperBCK-ideal of hyperBCK-algebra. Also we investigate that every positive implicative hyperBCK-algebra is a positive implicative hyperK-algebra and then we prove that every positive implicative hyperK-algebra is a weak positive implicative hyperk-algebra.

• Journal of the Chungcheong Mathematical Society
• /
• v.13 no.2
• /
• pp.29-39
• /
• 2001

For a Poisson Hopf algebra A, we find a natural Hopf structure in the Poisson enveloping algebra U(A) of A. As an application, we show that the Poisson enveloping algebra U(S(L)), where S(L) is the symmetric algebra of a Lie algebra L, has a Hopf structure such that a sub-Hopf algebra of U(S(L)) is Hopf-isomorphic to the universal enveloping algebra of L.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.2
• /
• pp.207-214
• /
• 2019

The notions of a fuzzy simple BCK/BCI-algebra and an (${\in},{\in}{\vee}q$)-fuzzy simple BCK/BCI-algebra are introduced. Using these notions, characterizations of a simple BCK/BCI-algebra are considered.

• Honam Mathematical Journal
• /
• v.31 no.3
• /
• pp.407-419
• /
• 2009

The simple non-associative algebra $N(e^{A_S},q,n,t)_k$ and its simple sub-algebras are defined in the papers [1], [3], [4], [5], [6], [12]. We define the non-associative algebra $\overline{WN_{(g_n,\mathfrak{U}),m,s_B}}$ and its antisymmetrized algebra $\overline{WN_{(g_n,\mathfrak{U}),m,s_B}}$. We also prove that the algebras are simple in this work. There are various papers on finding all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra (see [3], [5], [6], [9], [12], [14], [15]). We also find all the derivations $Der_{anti}(WN(e^{{\pm}x^r},0,2)_B^-)$ of te antisymmetrized algebra $WN(e^{{\pm}x^r}0,2)_B^-$ and every derivation of the algebra is outer in this paper.

• School Mathematics
• /
• v.4 no.1
• /
• pp.29-47
• /
• 2002

The purpose of this study is to investigate various perspectives on the approaching to school algebra. School algebra plays an important role in school mathematics, but many students have been in difficulties for the loaming of school algebra. This problem has been continued for the long time. This paper supposed that this problem may be caused by the approaching stage to the school algebra. In order to investigate this problem, we first described the definition of algebra in chapterII. And in chapterIII, we divided the perspectives of approaching to the school algebra into the two parts. The one is the intrinsic nature of algebra, i.e. generalization, abstraction, and structural aspects. The other is the extrinsic representation of algebra, i.e. problem solving, modelling, functions. Each perspectives are investigated through various research studies. We hope that this works on each perspectives help a teacher prepare school algebra.

• East Asian mathematical journal
• /
• v.29 no.4
• /
• pp.355-392
• /
• 2013

Generally school algebra is to start with introducing variables and algebraic expressions, which have major cognitive obstacles to students in the transfer from arithmetic to algebra. But the recent studies in the teaching school algebra argue the algebraic thinking from an early algebraic point of view. We compare the Korean elementary mathematics textbooks with Americans from this perspective. First, we discuss the history of school algebra in the school curriculum. And Second, we investigate the recent studies in relation to early algebra. We clarify the goals of this study(the importance of early algebra in the elementary school) through these discussions. Next we examine closely the number sense in the arithmetic and the symbol sense in the algebra. And we conclude that the operation sense can connect these senses within early algebra using the algebraic thinking. Finally, we compare the elementary mathematics books between Korean and American according to the components of the operation sense. In this comparative study, we identify a possibility of teaching algebraic thinking in the elementary mathematics and early algebra can be introduced to the elementary mathematics textbooks from aspects of the operation sense.

• Kyungpook Mathematical Journal
• /
• v.47 no.4
• /
• pp.549-568
• /
• 2007

In this paper we obtain a decomposition of certain factors of the signed Brauer algebra into a direct sum of simple algebras and we obtain the structure of the factor algebra.

• Honam Mathematical Journal
• /
• v.36 no.1
• /
• pp.179-186
• /
• 2014

In this paper, we consider the simple non-associative algebra $\overline{WN(\mathbb{F}[e^{{\pm}x^r},0,1]_{(\partial,\partial^2)})}$. There are many papers on finding the derivations of an associative algebra, a Lie algebra, and a non-associative algebra (see [2], [3], [4], [5], [6], [7], [12], [14]). We find all the derivations of the algebra $\overline{WN(\mathbb{F}[e^{{\pm}x^r},0,1]_{(\partial,\partial^2)})}$.

• Honam Mathematical Journal
• /
• v.40 no.2
• /
• pp.227-237
• /
• 2018

There are various papers on finding all the derivations of a non-associative algebra and an anti-symmetrized algebra. We find all the derivations of a growing algebra in the paper. The dimension of derivations of the growing algebra is one and every derivation of the growing algebra is outer. We show that there is a class of purely outer algebras in this work.

• The Mathematical Education
• /
• v.42 no.4
• /
• pp.481-501
• /
• 2003

The main purpose of this work is to propose programs of algebra courses for the department of mathematics education of teacher training universities. Set Theory, Linear Algebra, Number Theory, Abstract Algebra I, Abstract Algebra II, and Philosophy of Mathematics for School Teachers are discussed in this article.