• 제목/요약/키워드: algebra

검색결과 1,772건 처리시간 0.03초

AN ALGEBRA WITH RIGHT IDENTITIES AND ITS ANTISYMMETRIZED ALGEBRA

  • Choi, Seul-Hee
    • 호남수학학술지
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    • 제30권2호
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    • pp.273-281
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    • 2008
  • We define the Lie-admissible algebra NW$({\mathbb{F}}[e^{A[s]},x_1,{\cdots},x_n])$ in this work. We show that the algebra and its antisymmetrized (i.e., Lie) algebra are simple. We also find all the derivations of the algebra NW$(F[e^{{\pm}x^r},x])$ and its antisymmetrized algebra W$(F[e^{{\pm}x^r},x])$ in the paper.

대수 교육과정의 변화에 관한 고찰 - 패턴에 기초한 대수 도입을 중심으로 - (A study on the change of algebra curriculum - Focusing on the introduction of algebra based on patterns -)

  • 김성준
    • 대한수학교육학회지:수학교육학연구
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    • 제12권3호
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    • pp.353-369
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    • 2002
  • In this paper, we deal with the teaching of the approaching to algebra based on patterns. The change of algebra curriculum has been undergoing in many countries including USA, England, Australia. The traditional algebra curriculum starts with letters(variables), algebraic expressions, and equations. But these formal approaching method has many difficulties in teaching school algebra. Therefore the new algebra curriculum has to be needed, and the approaching to algebra based on patterns has been focused. In this paper, we compare this new approaching to algebra based on patterns to the traditional algebra curriculum. Next we consider the NCTM algebra curriculums based on Standards (1989) and Standards 2000(2000), Britannica textbook series(1998) based on RME. Also we investigate our pattern approaching in our curriculum and discuss some problems from the perspective of the approaching to algebra based on patterns.

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DERIVATIONS OF MV-ALGEBRAS FROM HYPER MV-ALGEBRAS

  • Hamidi, M.;Borzooei, R.A.
    • 호남수학학술지
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    • 제38권3호
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    • pp.643-659
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    • 2016
  • In this paper, we investigate some new results in MV-algebras and (strong) hyper MV-algebras. We show that for any infinite countable set M, we can construct an MV-algebra and a strong hyper MV-algebra on M. Specially, for any infinite totally bounded set, we can construct a strong hyper MV-algebra on it. Then by considering the concept of fundamental relation on hyper MV-algebras, we define the notion of fundamental MV-algebra and prove that any MV-algebra is a fundamental MV-algebra. In practical, we show that any infinite countable MV-algebra is a fundamental MV-algebra of itself, but it is not correct for finite MV-algebras.

ON HOMOMORPHISMS ON $C^*$-ALGEBRAS

  • Cho, Tae-Geun
    • 대한수학회보
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    • 제22권2호
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    • pp.89-93
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    • 1985
  • One of the most important problems in automatic continuity theory is to solve the question of continuity of an algebra homomorphism from a Banach algebra into a semisimple Banach algebra with dense range. Many results on this subject are obtained imposing some conditions on the domains or the ranges of homomorphisms. For most recent results and references in automatic continuity theory one may refer to [1], [4] and [5]. In this note we study some properties of homomorphisms from $C^{*}$-algebras into Banach algebras. It is shown that the range of an isomorphism from a $C^{*}$-algebra into a Banach algebra contains no non zero element of the radical of B. Using this result we show that the same holds for a continuous homomorphism, hence a Banach algebra which is the image of a $C^{*}$-algebra under a continuous homomorphism is necessarily semisimple. Thus if there is a homomorphism from a $C^{*}$-algebra onto a non-semisimple Banach algebra it must be discontinuous. Also it follows that every non zero homomorphism from a $C^{*}$-algebra into a radical algebra is discontinuous. Then we make a brief observation on the behavior of quasinilpotent element of noncommutative $C^{*}$-algebras in relation with continuous homomorphisms.momorphisms.

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대수의 탈산술화에 관한 고찰

  • 김성준
    • 한국수학사학회지
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    • 제16권1호
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    • pp.25-44
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    • 2003
  • In this paper, we deal with the ‘dearithmetization’ of algebra. Historically, the origin of algebra comes from arithmetic. Also school algebra is related to arithmetic in general. However, we have many difficulties in teaching school algebra, and there is many problems for students to learn algebra from elementary arithmetic knowledges. This paper supposed that the solution of these problem may be founded in the ‘dearithmetization’ of algebra. And we supposed that the ‘dearithmetization’ of algebra may be developed by three historical achievements - the completion of symbolic algebra, the principle of permanence of form, and the expansion of number concepts. In order to justify these supposition, we investigate Peacock's ideas, i.e. ‘symbolic algebra’, ‘the principle of permanence of form’, and consider how the integer is introduced in modern mathematics. And we analyze various textbooks, and investigate the ‘dearithmetization’ of school algebra which has been progressed in the three fields - symbolic algebra, the principle of permanence of form, and the expansion of number concepts.

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COMPLETELY V-REGULAR ALGEBRA ON SEMIRING AND ITS APPLICATION IN EDGE DETECTION

  • G.E. CHATZARAKIS;S. DICKSON;S. PADMASEKARAN;J. RAVI
    • Journal of applied mathematics & informatics
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    • 제41권3호
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    • pp.633-645
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    • 2023
  • In this paper, Completely V-Regular on semiring is defined and used to derive new theorems with some of its properties. This paper also illustrates V-Regular algebra and Completely V-Regular Algebra with examples and properties. By extending completely V-Regular to fuzzy, a new concept, fuzzy V-Regular is brought out and fuzzy completely V-Regular algebra is introduced too. It is also developed by defining the ideals of Completely V -Regular Algebra and fuzzy completely V-Regular algebra. Finally, this fuzzy algebra concept is applied in image processing to detect edges. This V-Regular Algebra is novel in the research area.

A REMARK ON THE CONJUGATION IN THE STEENROD ALGEBRA

  • TURGAY, NESET DENIZ
    • 대한수학회논문집
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    • 제30권3호
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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 ${\chi}^{\prime}$.

DERIVATIONS OF A COMBINATORIAL LIE ALGEBRA

  • Choi, Seul Hee
    • 호남수학학술지
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    • 제36권3호
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    • pp.493-503
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    • 2014
  • We consider the simple antisymmetrized algebra $N(e^{A_P},n,t)_1^-$. The simple non-associative algebra and its simple subalgebras are defined in the papers [1], [3], [4], [5], [6], [8], [13]. Some authors found all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra in their papers [2], [3], [5], [7], [9], [10], [13], [15], [16]. We find all the derivations of the Lie subalgebra $N(e^{{\pm}x_1x_2x_3},0,3)_{[1]}{^-}$ of $N(e^{A_p},n,t)_k{^-}$ in this paper.