• 대한수학회논문집
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• 제27권2호
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• pp.217-222
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• 2012

In this note we investigate some properties of ${\beta}$-algebras and further relations with $B$-algebras. Especially, we show that if ($X$, -, +, 0) is a $B^*$-algebra, then ($X$, +) is a semigroup with identity 0. We discuss some constructions of linear ${\beta}$-algebras in a field $K$.

• 호남수학학술지
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• 제41권2호
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• pp.435-447
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• 2019

The notions of a neutrosophic subalgebra and a neutrosohic ideal of a subtraction algebra are introduced. Characterizations of a neutrosophic subalgebra and a neutrosophic ideal are investigated. We show that the homomorphic preimage of a neutrosophic subalgebra of a subtraction algebra is a neutrosophic subalgebra, and the onto homomorphic image of a neutrosophic subalgebra of a subtraction algebra is a neutrosophic subalgebra.

• 한국정보과학회논문지:시스템및이론
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• 제27권3호
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• pp.337-344
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• 2000

본 논문에서는 다중자원(multiple resource)을 사용하는 시스템의 명세와 검증을 위한 프로세스 대수 ACSMR(Algebra of Communicating Shared Multiple Resources)을 정의한다. ACSMR은 프로세스 대수 기반의 정형기법(formal methods)인 ACSR에 다중자원의 개념을 확장한 것이다. 명세와 검증의 예로 실시간 시스템의 스케줄링 기법의 하나인 Earliest-Deadline-First(EDF)를 멀티프로세서하에서의 시스템의 행동 명세와 다중 포트를 가진 레지스터를 이용한 수퍼스칼라 프로세서의 타이밍 특성과 자원 제한을 묘사하기 위한 명세방법을 제시한다.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.1129-1135
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• 2022

The purpose of this research is to find an extension of the renowned Chernoff theorem on standard operator algebra. Infact, we prove the following result: Let H be a real (or complex) Banach space and 𝓛(H) be the algebra of bounded linear operators on H. Let 𝓐(H) ⊂ 𝓛(H) be a standard operator algebra. Suppose that D : 𝓐(H) → 𝓛(H) is a linear mapping satisfying the relation D(AⁿBⁿ) = D(Aⁿ)Bⁿ + AⁿD(Bⁿ) for all A, B ∈ 𝓐(H). Then D is a linear derivation on 𝓐(H). In particular, D is continuous. We also present the limitations on such identity by an example.

• 충청수학회지
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• 제23권2호
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• pp.323-333
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• 2010

The biproduct bialgebra has been generalized to generalized biproduct bialgebra $B{\times}^L_H\;D$ in [5]. Let (D, B) be an admissible pair and let D be a bialgebra. We show that if generalized biproduct bialgebra $B{\times}^L_H\;D$ is a Hopf algebra with antipode s, then D is a Hopf algebra and the identity $id_B$ has an inverse in the convolution algebra $Hom_k$(B, B). We show that if D is a Hopf algebra with antipode $s_D$ and $s_B$ in $Hom_k$(B, B) is an inverse of $id_B$ then $B{\times}^L_H\;D$ is a Hopf algebra with antipode s described by $s(b{\times}^L_H\;d)={\Sigma}(1_B{\times}^L_H\;s_D(b_{-1}{\cdot}d))(s_B(b_0){\times}^L_H\;1_D)$. We show that the mapping system $B{\leftrightarrows}^{{\Pi}_B}_{j_B}\;B{\times}^L_H\;D{\rightleftarrows}^{{\pi}_D}_{i_D}\;D$ (where $j_B$ and $i_D$ are the canonical inclusions, ${\Pi}_B$ and ${\pi}_D$ are the canonical coalgebra projections) characterizes $B{\times}^L_H\;D$. These generalize the corresponding results in [6].

• 충청수학회지
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• 제8권1호
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• pp.37-44
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• 1995

In this paper we show that every left derivation on a semiprime Banach algebra A is a derivation which maps A into the intersection of the center of A and the Jacobson radical of A, and hence every left derivation on a semisimple Banach algebra is zero.

• 대한수학회논문집
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• 제12권4호
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• pp.911-920
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• 1997

This note centers around the class M(A) of multipliers on a Gelfand algebra A. This class is a large subalgebra of the Banach algebra L(A). The aim of this note is to investigate some aspects concerning their local spectral properties of multipliers. In the last part of work we consider some applications to automatic continuity theory.

• 대한수학회논문집
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• 제18권2호
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• pp.225-233
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• 2003

In this paper, we obtain Hon(P,- ) is an exact functor if P is a p-projective BCI-algebra.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.333-340
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• 2010

We estimate the real rank of a composition series of closed ideals of a $C^*$-algebra such that its subquotients have continuous trace, which is equivalent to that the $C^*$-algebra is of type I.

• 한국수학사학회지
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• 제23권2호
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• pp.89-99
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• 2010

오늘날 선형대수학은 이론의 기초적 성격과 응용의 풍부성으로 인해 대학수학에 있어서 필수적인 분야로서 자리하고 있다. 벡터이론과 행렬이론은 선형대수학의 주된 분야이다. 본 논문에서는 선형대수학의 학습에서 벡터이론과 행렬이론 중 어느 것을 먼저 도입하는 것이 바람직할 것인가에 대한 질문을 제시할 때 본 연구의 주된 결과, 역사적 순서와는 달리 벡터이론이 행렬이론보다 선행되어야 함을 주장한다.