• Honam Mathematical Journal
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• v.29 no.4
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• pp.495-509
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• 2007

In this note it is proved that MPR is rigid as a Hopf algebra with distinguished basis. I.e. there are no nontrivial automorphisms that preserve the multiplication and comultiplication and take the distinguished basis of all permutations into itself (as a graded set).

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.191-195
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• 2001

In this paper, a simple axiom system of lattice implication algebras is presented, it is convenient for verifying whether an algebra of type (2,2,2,1,0,0) becomes a lattice implication algebra.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.365-371
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• 1999

In this paper, we prove that the range of homomorphism from a C\ulcorner-algebra A into a commutative Banach algebra B whose radical is nil contains no non-zero element of the radical of B. Using this result we show that there is no non-zero homomorphism from a C\ulcorner-algebra into a commutative radical nil Banach algebra.

• Industrial Engineering and Management Systems
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• v.3 no.1
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• pp.1-11
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• 2004

This paper proposes a new algorithm for determining an optimal control input for production systems. In many production systems, completion time should be planned within the due dates by taking into account precedence constraints and processing times. To solve this problem, the max-plus algebra is an effective approach. The max-plus algebra is an algebraic system in which the max operation is addition and the plus operation is multiplication, and similar operation rules to conventional algebra are followed. Utilizing the max-plus algebra, constraints of the system are expressed in an analogous way to the state-space description in modern control theory. Nevertheless, the formulation of a system is currently performed manually, which is very inefficient when applied to practical systems. Hence, in this paper, we propose a new algorithm for deriving a state-space description and determining an optimal control input with several constraint matrices and parameter vectors. Furthermore, the effectiveness of this proposed algorithm is verified through execution examples.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.165-178
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• 2022

In this paper, Sheffer stroke BL-algebra and its properties are investigated. It is shown that a Cartesian product of two Sheffer stroke BL-algebras is a Sheffer stroke BL-algebra. After describing a filter of Sheffer stroke BL-algebra, a congruence relation on a Sheffer stroke BL-algebra is defined via its filter, and quotient of a Sheffer stroke BL-algebra is constructed via a congruence relation. Also, it is defined a homomorphism between Sheffer stroke BL-algebras and is presented its properties. Thus, it is stated that the class of Sheffer stroke BL-algebras forms a variety.

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

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.627-634
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• 2006

A Weyl type algebra is defined in the book ([4]). A Weyl type non-associative algebra $\={WP_{m,n,s}}$ and its restricted sub-algebra $\={WP_{m,n,s_{\gamma}}}$ are defined in various papers ([1], [12], [3], [11]). Several authors 0nd all the derivations of an associative (Lie or non-associative) algebra in the papers ([1], [2], [12], [4], [6], [11]). We find all the non-associative algebra derivations of the non-associative algebra $\={WP_{0,2,0_B}$, where $B=\{{\partial}_0,\;{\partial}_1,\;{\partial}_2,\;{\partial}_{12},\;{\partial}^2_1,\;{\partial}^2_2\}$.

• Journal of Educational Research in Mathematics
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• v.12 no.1
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• pp.29-48
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• 2002

The purpose of this paper is to investigate the transfer in mathematics learning, especially focussing on arithmetic and algebra. There are many obstacles at the stage of transfer in learning. In the case of mathematics, each learning contents are definitely categorized by the learning level, therefore these obstacles are more happened than other subjects. First of all, this paper investigates the historical transfer from arithmetic to algebra by Sfard's perspectives. And we define prealgebra as the stage between arithmetic and algebra, which may be revised obstacles or misconceptions happened in the early algebra learning. Also, this paper discusses various obstacles and concrete examples happened in the transfer from arithmetic to algebra. To advance the understanding in the learning of algebra, we consider the core contents of the algebra learning which should be stressed at the prealgebra stage. Finally we present the teaching units of (pre)algebra which are sequenced from the variable concepts to equations.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.559-564
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• 2013

In this paper we investigate necessary conditions for the mirror algebra $(M(X),{\bigoplus},(0,0))$ to be a $d$-algebra (having the condition (D5), resp.) when (X, *, 0) is a d-algebra (having the condition (D5), resp.). Moreover, we obtain the necessary conditions for M(X) of a $d^*$-algebra X to be a $d^*$-algebra.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.527-541
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• 2001

We find the necessary and sufficient conditions for the smash product algebra structure and the crossed coproduct coalgebra structure with th dual cocycle $\alpha$ to afford a Hopf algebra (A equation,※See Full-text). If B and H are finite algebra and Hopf algebra, respectively, then the linear dual (※See Full-text) is also a Hopf algebra. We show that the weak coaction admissible mapping system characterizes the new Hopf algebras (※See Full-text).