• 대한수학회보
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• 제52권5호
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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.

• 대한수학회논문집
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• 제10권1호
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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.

• 대한수학교육학회지:수학교육학연구
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• 제17권3호
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• pp.253-270
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• 2007

18세기 프랑스의 수학자 A.C. Clairaut는 역사발생적 원리에 근거하여 기하 교재에 이어 대수 교재 <대수학 원론>을 집필하였다. 본 논문은 <대수학 원론>을 분석함으로써 대수 지도를 위해 Clairaut가 의도한 원리 및 구체적인 방식의 특징들을 고찰하고, 학교 수학에서 대수 영역의 교수-학습과 비교, 논의함으로써 적용 가능한 교수학적 시사점을 찾는 것을 목표로 한다. 이를 위해 <대수학 원론>의 구성 및 내용에 대해 개관하고 초보자의 정신에 자연스럽게 전개한다는 Clairaut의 의도에서 비롯된 대수 지도 원리의 여섯 가지 특징을 추출한다. 이 중에는 <기하학 원론>에서의 특징과 공통적인 것도 있고 대수라는 내용 영역상의 구별에서 비롯되는 독특한 것도 있다. 그리고 학교 수학의 대수 영역 중 특정 주제-방정식 세우기, 문자식의 계산과 문자의 부호, 곱셈의 부호 규칙, 이차방정식의 해법, 근과 계수와의 일반적 관계-와 관련하여 논의하고 시사점을 찾는다.

• East Asian mathematical journal
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• 제21권1호
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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].

• 호남수학학술지
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• 제41권2호
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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.

• 대한수학회논문집
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• 제17권2호
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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.

• 충청수학회지
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• 제1권1호
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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.

• 충청수학회지
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• 제32권1호
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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.

• 대한수학회논문집
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• 제12권1호
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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.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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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.