• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1587-1606
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• 2015

Comonoid, bi-algebra, and Hopf algebra structures are studied within the universal-algebraic context of entropic varieties. Attention focuses on the behavior of setlike and primitive elements. It is shown that entropic $J{\acute{o}}nsson$-Tarski varieties provide a natural universal-algebraic setting for primitive elements and group quantum couples (generalizations of the group quantum double). Here, the set of primitive elements of a Hopf algebra forms a Lie algebra, and the tensor algebra on any algebra is a bi-algebra. If the tensor algebra is a Hopf algebra, then the underlying $J{\acute{o}}nsson$-Tarski monoid of the generating algebra is cancellative. The problem of determining when the $J{\acute{o}}nsson$-Tarski monoid forms a group is open.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.123-131
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• 1995

The notion of our non-associative algebra is obtained from the Lotka-Volterra system of differential equation describing competitiion between animals or vegetals species and also in the kinetic theory of gasses. For the structure of an algebra, the existence of idempotents is of particular interest. But also from the biological aspect the existence of such elements is of interest because the equilibria of a population which can be described by an algebra correspond to idempotents of this algebra. Thus we present some properties of the general natures for a Lotka-Volterra algebra associated to a weight function and idempotents elements.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.253-270
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• 2007

by A.C. Clairaut was written based on the historico-genetic principle such as his . In this paper, by analyzing his we can induce six principles that Clairaut adopted to teach algebra: necessity and curiosity as a motive of studying algebra, harmony of discovery and proof, complementarity of generalization and specialization, connection of knowledge to be learned with already known facts, semantic approaches to procedural knowledge of mathematics, reversible approach. These can be considered as strategies for teaching algebra accorded with beginner's mind. Some of them correspond with characteristics of , but the others are unique in the domain of algebra. And by comparing Clairaut's approaches with school algebra, we discuss about some mathematical subjects: setting equations in relation to problem situations, operations and signs of letters, rule of signs in multiplication, solving quadratic equations, and general relationship between roots and coefficients of equations.

• East Asian mathematical journal
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• v.21 no.1
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• pp.49-60
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• 2005

In this paper we introduced Semi-neutral BCK-algebra and investigate some of its properties. The notions of ideals and subalgebras coincide in Semi-neutral BCK-algebras. We also show that if the number of nonzero elements in a Semi-neutral BCK-algebra is n, then the number of ideals/subalgebras in it is $2^n$. Further, we solved an open problem posed by W.A. Dudek in [2].

• Honam Mathematical Journal
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• v.41 no.2
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• pp.421-433
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• 2019

Let n denote an integer greater than 2 and let c denote a nonzero complex number. In this paper, we introduce a family of elements of the rational Cherednik algebra $H^{sl_n}(c)$ of type $sl_n$, which are analogous to the Dunkl-Cherednik elements of the rational Cherednik algebra $H^{gl_n}(c)$ of type $gl_n$. We also introduce the raising and lowering element of $H^{sl_n}(c)$ which are useful in the representation theory of the algebra $H^{sl_n}(c)$, and provide simple results related to these elements.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.237-243
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• 2002

In this paper we generalize the Lie algebras of KPS's in [4], which have no toral elements. However our generalized Lie algebras have toral elements. Moreover our Lie algebras are not isomorphic to the Witt algebra W(n) with a toral element.

• Journal of the Chungcheong Mathematical Society
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• v.1 no.1
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• pp.33-41
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• 1988

In this paper, the abelian property of Hermitian elements holds not generally in Banach algebra, but in the case that some conditions satisfy, they are abelian. By using property of [1], [2], the Hermitian elements a and b in Banach algebras have been shown that ab = ba.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.53-67
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• 2019

The notions of closed elements and dense elements are introduced in BE-algebras. Characterization theorems of closed elements and closed filters are obtained. The notion of dense elements is introduced in BE-algebras. Dense BE-algebras are characterized with the help of maximal filters and congruences. The concept of D-filters is introduced in BE-algebras. A set of equivalent conditions is derived for every D-filter to become a closed filter.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.45-50
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• 1997

The purpose of this paper is to give a characterization of automorphisms of the weighted Lotka-Volterra algebra $(A,\omega)$ at idempotent elements and to offer a condition that $(A,\omege)$ becomes a Jordan algebra.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.531-536
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• 1998

It is well known that a Boolean algebra is one of the most important algebra for engineering. A fuzzy algebra, which is referred to also as a Kleen algebra, is obtained from a Boolean algebra by replacing the complementary law in the axioms of a Bloolean algebra with the Kleen's law, where the Kleen's law is a weaker condition than the complementary law. Removal of the Kleen's law from a Kleen algebra gives a De Morgan algebra. In this paper, we generate lattice structures of the above related algebraic systems having finite elements by using a computer. From the result, we could find out a hypothesis that the structure excepting for each element name between a Kleene algebra and a De Morgan algebra is the same from the lattice standpoint.